Clouds work both ways: They reflect short-wave visible radiation back into space, but they also send long-wave thermal radiation back to the ground and keep it warmer (compare your experience with cloudless nights to ones with clouds).

So far it looks like high clouds have a cooling effect and low clouds have a warming effect. We are not sure yet which clouds will increase more (this may not be up-to-date or might be known soon) but we expect more clouds in general in a warmer climate.