Does visible light heat things up?

Yes, it would, though not as quickly as if you were getting the full spectrum of sunlight. All frequencies of the light spectrum carry energy, so it becomes a question of how much of that energy is absorbed by the house.

For example, if your house was completely black, all that visible light energy would be absorbed by the house and converted into heat. If it was completely white (or massively reflective), there would be almost no heat transfer whatsoever.