The air will conduct heat, but not very well, it is very thin, very dry and very cold.
Mars rotates at an angle of about 25Degrees, Earth is about 23Degrees, the closest bright star to the pole would be Deneb, which is in Cygnus, but I don’t think it is very close to the pole.
Mars does have seasons, but they would be about twice as long as ours as a year on Mars is about 687 Earth Days. You can actually see the polar ice on mars advancing and retreating with the seasons from Earth with a decent telescope. I would expect that you could in fact keep track of that with about $600 worth of telescope and a sketch pad