writers interested in learning about the conditions necessary for habitable planets should read Habitable Planets for Man, Stephen H. Dole, 1964, 2007. Otherwise they will risk being over fifty years behind the times in some of the stories they write.
I am assuming that the natives of Cyromoreth are carbon based lifeforms using w liquid water as their biochemical solvent, and thus have biochemestry and enviromental requirements similar to those of humans. If the Cryomonians actually use liquid methane as their solvent in life processes some of my conclusions may not be totally valid.
Here is a link to another question:
https://worldbuilding.stackexchange.com/questions/190628/my-planet-has-a-long-period-orbit-how-can-i-make-the-seasons-change-faster-in-o/190660#190660[1]
The question is about a planet in a 6.78 year long orbit. That is not six hundred and seventy eight Earth years, but six point seven eight Earth years.
And my answer to that question casts doubt on whether it would be possible to have a planet habitable for humans or other Earth life (and not habitable for Eich or Palainians who live on very cold planets and have a totally different biochemistry than Earth life) with a year that is as long as six point seven eight Earth years long.
And now you ask about whether a planet with a year 273.15 Earth years long - which is 40.287 times 6.78 Earth years - orbiting a star with about one solar mass could have temperatures a lot hotter than Earth at some times and a lot colder than Earth at other times and thus averging close to Earth temperatures.
The lowest temperature recorded on Earth is - 89.2 C, or - 128.6 F, or 184.0 K. The average temperature on Earth in 2017 was about 58.62 F, or 14.9 C, or 288.05 K. The highest temperature on Earth was 54.0 C, or 129.2 F, or 327.15 K.
The difference between 184.0 K and 327.15 K is 143.15 degrees K. Half of that is 71.575 degrees K. Adding that to the lowest temperature recorded on Earth gives a temperature of 255.575 K, not too far from the average temperature of 288.05 K in 2017.
The question asks for a planet with a temperature ranging from 270 K to 313 K. That is a difference of 43 K. Half of that is 21.5 degrees K. Adding that to 270 K gives a more or less average temperature of about 291.5 K, or 18.35 C, or 65.03 F.
Thus the planet Cryomoreth would have more or less average temperature slightly higher than Earth's average temperature in 2017 while orbiting a star of similar mass to the Sun with a year 273.15 Earth years long. Since radiation from the Sun is the source of almost all of Earth's surface heat, it should be obvious that is almost totally impossible.
Planets will not have a constant enough surface temperature to remain habitable for life for the billions of years necessary for intelligent life to evolve unless those stars are main sequence stars shining with relatively steady luminosity for geologic eras of time.
The mass of a star mainly determines how luminous it will be when on the the main sequence, though its chemical composition and age will also affect its luminosity. All main sequence stars with the mass of the Sun will have about the same luminosity as the Sun while on the main sequence. So having a planet orbit a main sequence star with the mass of the Sun and a year 273.15 tiems as long as the Earth's year - and thus orbiting mmuch farther from that star - and yet having a temperature range similar to that of Earth, is pretty much impossible.
There is one way out. After the end of the period when the Sun is a main sequence star, it will swell up to a red giant stars, and its luminosity will multiply. Thus a planet which used to be bitterly cold and too cold for Earth type lifewith will become much warmer, perhaps warm enough to have the same temperature range and average temperature as desire for Cyromoreth.
Even before it becomes a red giant, the luminosity of the Sun will have nearly doubled, and Earth will receive as much sunlight as Venus receives today. Once the core hydrogen is exhausted in 5.4 billion years, the Sun will expand into a subgiant phase and slowly double in size over about half a billion years. It will then expand more rapidly over about half a billion years until it is over two hundred times larger than today and a couple of thousand times more luminous. This then starts the red-giant-branch phase where the Sun will spend around a billion years and lose around a third of its mass.[129]
https://en.wikipedia.org/wiki/Sun#After_core_hydrogen_exhaustion[2]
So the Sun will be a red giant star with about 2,000 times its present luminosity for about one billion years, billions of years in the future. The distance from the Sun in the red giant phase that a planet would have to orbit in order to receive about as much radiation from the Sun as Earth does now should be about the square root of 2,000 times one Astronomical Unit (AU) the radius of Earth's orbit.
The square root of about 2,000 would be about 44.721, so if Cryomoreth orbits a red giant star with about the mass of the Sun and about 2,000 times the present luminosity of the Sun it would have to orbit at a distance of about 44.721 AU from its star. The length of Cryomoreth's year would be the same as the year of a planet orbiting the Sun at distance of about 44.721 AU.
The outermost planet in our solar system, Neptune, orbits the Sun with a perihelion of 29.81 AU and an aphelion of 30.33 AU, and a semi-major axis of its orbit of 30.7 AU, and has a year 164.8 Earth years long.
A better comparison is the former planet Pluto, which has a perihelion of 29.668 AU and an aphelion of 40.309 AU, and a semi-major axis of its orbit of 39.482 AU, and has a year 247.94 Earth years long. Pluto has a highly eccentric orbit like Cryomoreth.
The dwarf planet Haumea is a closer fit to Cryomoreth than Pluto is. It has a perihelion of 34.767 AU and an aphelion of 51.989 AU, and a semi-major axis of its orbit of 43.181 AU, and has a year 283.77 Earth years long. Haumea has a highly eccentric orbit like Cryomoreth.
So as a first order approximation of cryomoreth, a planet large enough to be habitable, with an orbit similar to that of Haumea, could have a year length similar to that of Cyromoreth and possibly expience the temperature range desired for Cyromoreth, while orbiting a star with the mass of the Sun - when, and only when, that star is in the red giant phase of its evolution and shines with a luminosity of about 2,000 times that of the Sun.
I must say that when I started this answer I didn't expect that a world like Cyromoreth would be as possible as my rough calculations indicate.
But there is one flaw with this. The Sun is expected to be a red giant for about one billion (1,000,000,000) years. That is an unimaginably long time period. However, it took Earth several times as long to becaome habitable for large oxygen breathing animals. So if life on Cyromoreth begains only when it is heated by the red giant star, that star should not remain a red giant star long enough for intelligent life to evole on it.
One way to get around that would be have an extremely advanced civilization move the planet Cryomoreth, which aleady has lifeforms, from closer to its star to a much wider orbit as its star expands in luminosity, thus enabling the lifeforms on Cryomoreth to continue living and evolving and eventually evolve intelligent life.
Why not ditch the requirement that Cyromoreth orbit a star with the mass of the Sun, and have cryomoreth orbit a much more massive main sequence star with thousands of time the luminosity of the Sun. There are a very few stars with luminosity over a million tiems that of the Sun, on the habitable zone of those stars should be about a thousand times as far from those stars as the habitable zone of the Sun is. So a star would not have to be the most massive and luminous star known to have planets in its habitable zone which had years even longer than 273.15 Earth years.
But those stars use up their nuclear fuel extremely fast. Calculations indicate that the most massive and luminous main sequence stars which might last long enough to have their planets become habitable for humans or beings with similar requirements, would be spectral class F main sequence stars, and the the most luminous of them are only a few times as luminous as the Sun, certainly not luminous enough to have years more than a tiny fraction of 237.15 Earth years long.
writers interested in learning about the conditions necessary for habitable planets should read Habitable Planets for Man, Stephen H. Dole, 1964, 2007. Otherwise they will risk being over fifty years behind the times in the stories they write.
