Seeking advice to minimize stress to Leo

I recently moved into a apartment where my roommate owned a leopard gecko. Having some knowledge on the care of herpes, mainly snakes and turtles, I though my roommate might be mistreating her leo. After talking to her about it she agreed to let me take him over. He is now getting upgraded from a 10 gallon tank to a 20 gallon, is upgrading from one hide (cold) to three (cold, moist, hot), and will very soon have a heating elements for his tank (under tank heater, and lamp). All of the things I ordered for him are arriving on 3/23. My concern and question to the community here is that; This Leo has never had a heated tank. The apartment is generally in the low-mid 50's in the wintertime. My understanding is that my roommate has kept him this way for a year. He is very lethargic right now due to the cold. I worry that moving him into a heated tank on the 3/23 will cause more stress to his already stressed out system. I don't want to do him more harm than good by suddenly changing the temp of his surroundings. Is this a valid concern for a leo? or should I trust that he will move around in his new tank to regulate his own temp. accordingly?

It should also be noted that I believe that this leo is very underweight. I think my roommate only feeds him once every 2-3 weeks in the winter. He is so cold he shows very little interest in eating for her and so she did not feed him the recommended every 2-3 days. Also he was not receiving regular fresh water.

I know that this leos situation is very upsetting. I am doing everything I can to get him situated the way he should have been in since day one. Any advice from breeders or individuals who have raised/owned leos would be appreciated.

If you plug in the UTH and put the leo in the cage, it will take a number of hours before it heats up completely (remember to get a thermostat so it doesn't get too hot), so he'll have time to get used to it. Also, the reason you put the heat on one side is to have a heat gradient. If he isn't comfortable with the heat at first, he can stay on the cool side. I wouldn't be surprised if he goes for the heat since I think it's more of an instinct. You don't really need the lamp as long as there is ambient light in the room. If he's cold, he will not eat much and will also not digest it well, so hopefully you'll see a gradual change in the new environment.
Welcome to GF!

Aliza