Technically speaking, If you managed to create a planet with an ideal gas atmosphere, the atmosphere would just float away. Why?
One of the approximations of an ideal gas is
- There are no attractive or repulsive forces between the molecules or the surroundings
This means that the gas wouldn't feel the force of gravity!
So if I had a jar of ideal gas, the pressure wouldn't increase as I went to a greater depth in the jar(It does increase in gasses too, just like it does in liquids).
I know this sounds strange but all it really means is that you cannot apply the ideal gas approximation to a system the size of our atmosphere. This approximation works well for small systems(A jar of ideal gas), because the effects of gravity are pretty negligible.
So to analyse effects of change in temperature on the whole atmosphere, you'll need a better model. Maybe considering the atmosphere a non-viscous fluid can help, I don't know. You should research on this.
Note that other approximations like the Van der Waals equation wouldn't help too because they too neglect the effect of gravity.