Tough situation....
If you're trying to break her of being broody, best to take that bedding out of there.
You want to 'cool her off', but she's right next to the radiator, plus the house is so much warmer than outside.
Will be curious as to how this works out.
Just a new location may break her 'broody', then you can put her back outside.
Best of cLuck!
Where in this world are you located?
Climate, and time of year, is almost always a factor.
Please add your general geographical location to your profile.
It's easy to do, (laptop version shown), then it's always there!