My wife uses a simple black terrycloth hand towel, we keep one in the tour pack. She wraps it over the top, tucks it in and drapes it down the backrest. Inexpensive, easy to carry and easy to wash.
Depends a lot on what she wears. Different clothes next to her skin (just a moment......I'm OK now) and over the top can improve comfort and reduce her problem. Either plenty of cotton, or if you believe the adverts, modern wicking materials can work wonders. Leaving her at home is a bit radical and could have unintended consequences!
Yeah, as said, throw a piece of sheepskin over the back. Does her *** also get hot on the seat? If so, sheepskin works there also. Make sure you have the furry side up.