If you buy a heated bed for the cat, you will be surprised to see how she takes to it.
Anyone considering it should remember something about cats though, don’t show her the bed and let her know that you want her to get on it, if you do, she will avoid it.
The cat has to discover things on their own usually, or that stubborn streak might come out, the one where they do things to spite you, like totally ignoring the toy you brought home for them, the same toy that they will seek out and love if you pretend that it has nothing to do with them.
They can be perverse creatures-I used to offer my cats the toys I bought, but after seeing the behavior you refer to, now I just nonchalantly toss the new toys someplace where they can be easily seen-mine are especially fond of those little fur mice-there are at least 15 of the things on the floor and on furniture where they have been carried...
I’m definitely going to invest in one of those heated beds when I have a few bucks available...