The title is my question. Does the ground effect change as the temperature of the ground changes? In cold weather, a more cushion effect can be expected, and in hot weather vice versa?
No. There is nothing in the physics of ground effect that depends on temperature.
On a hot day, you will have higher density altitude. Your true approach speed will be greater (for the same equivalent airspeed). You may perceive a difference in the way the landing feels because you are moving faster across the ground, but there is no difference in ground effect.
Also, on a hot day, thermals can form over dark areas of ground. This convective activity can cause an aircraft on final to float.
I will assume:
- You are asking about the temperature of the air near the ground, not the temperature of the ground itself.
- The ground effect is the pressure caused by compression of air between the wing and the ground.
- The ambient pressure does not depend on the temperature and the ground effect is isentropic.
The temperature of the air near the ground has a quite small relationship to the ground effect. The ground effect can be simplistically described with the isentropic compressibility, which is inversely related to the square of the speed of sound. As temperature increases, the speed of sound increases slightly. This would cause an increase in ground effect. The difference would be too small to be relevant to pilots or aircraft designers.
If you accounted for turbulence and phase changes (such as water condensing) then you may see other differences due to deviation from the ideal gas law. These may be slightly less tiny near the melting point of water.