Question

What would happen to temperatures on earth the suns heat were distributed throughout the atmosphere

Answer 1

For example, California's water cycle was on hold because we did not have any rain. The weather has been dry warm, so all of the water is being evaporated, but never reaching the precipitation phase of the cycle.

Answer 2

If the sun's heat is distributed uniformly throughout the atmosphere, this will ensure that each point on the earth gets a moderate level of heat and temperature in these locations will be within the acceptable level.
If the sun's heat is concentrated in one part of the atmosphere, the location that correspond to the point of concentration will receive enormous amount of heat from the sun, which will shoot up the temperature of that location. This will leads to all manner of disruptions in the ecosystem that is found in that location.