It is safe to cover your cage, just be careful if you have the lights on a timer and I will tell you why. I used to cover the cage over the top right on top of the lights and would usually get up before the lights went on. One day I slept in and I went into check the cage. The lights were on and the cover was starting to burn on top of one of the dome lights! It was one of the black ceramic ones and it gets hot! I was totally freaked out cause I know what could have happened had I not woken up. So I wrap the sides now with a big blanket that does not involve the lights! Just one of those stupid little woulda, shoulda coulda's that could have turned into a disaster.