Yes, I do, for the sake of her health and her eventual psychological well being.
"I dont think she'd like that and I want her to be happy and comfortable."
She's making bad decisions, relying on her familiarity of your home to find dark(cold), unsuitable hides. As her guardian, she needs you to protect her from that.
IMO when you close the doors on her, she could well feel physically better, allowing her to adapt in less time. Her appetite should increase in the warmer climate. She's going to get used to all this after a while anyway, so why not make this more healthy for her. Let her settle for being with you for short periods as this settles out.
When she sulks in the cool zone of her hab, can you reach in and put her on her basking shelf? That is what I'd do for the next two weeks, until she uses the basking spot enough on her own. Then I would let her take short forays outside as long as you cut it short and put her back.