If I sit still I get way more sensitive to temperature than if I move around. Like lying under a warm duvet, it's almost impossible to remove it. But get up and do some frog leaps and burpees and you'll soon want to throw off that duvet and change your situation.
Same with shivering in a cold wet towel, being cold isn't enough to get me to get dressed if I'm sitting down. But doing some squats or hip raises to raise my body temperature and suddenly I'm able to move around and get shit done again.
My brain is motion powered. I need to move to function.
Find some movement you can do in bed (hip raises, crunches, pushups) that get you warm enough to get out of bed. Maybe it helps!