The lack of UV is not really the issue. Just like a baby, you need to make sure the environment is safe for him to wander in. Look for stuff he may try to eat. Seems crazy, but mine have tried to eat carpet and whatever else they find before! You don't want to let him eat stuff, and believe me if he thinks it is food, he'll try to eat it.
Lie on your floor naked and see how the temperature is. That's what your tort will feel. I think this is only ok in rare circumstances such as the floor is very warm, it's clean hard wood (even a hair can be hazardous), supervised like a hawk, etc. Most of the time they are cold and scared, looking for a place to hide. I wouldn't recommend it. They don't think it's fun because they are away from the comforts of home, and just want a place to feel secure--that is why they will "run" around, because they want to find a hiding space in the great expanses of the house. Also, the more you expose them to huge open spaces the more they will crave that vs. their "small" enclosure, comparatively.
They can be away from UV for awhile before it will warm there. Heat and hazards are more the issue. My tort likes to spend more of his days in the 80s in his enclosure. Most of the year my house is in the low 70s. Not so great for him.
I created a home away from home rubbermaid tub for my tort I use to put him outside (where we watch him), in the living room if we just want to give him an outing and its too cold outside, and the vet. Works great and is safe for him and he's gotten used to it. It has his bedding and a hide, but he's not in there long enough to need water and food.