* Sunlight is hot: The sun produces light and heat through nuclear fusion, a process that releases enormous amounts of energy.
* Reflection doesn't generate heat: When the moon reflects sunlight, it's simply bouncing that energy back into space. The reflected light carries less energy than the original sunlight, and therefore doesn't create significant heat.
Think of it like a mirror. A mirror reflects light, but it doesn't get hot from doing so. The same principle applies to the moon.
So, while sunlight is very hot, the moon's light is just reflected sunlight and thus doesn't contain enough energy to feel warm.