[Edi]

The only non-fire sites that produce heat are Banefire Braziers and Rain Forest. If you haven't Augured the province or done F4 searches, there's Prison of the Desert Sun that increases the heat scale by 6 (Yes, it increases heat TWICE!) So even with a Cold 3 dominion and repeated Wolven Winter castings you would stay at high heat unless you also had a cold scale increasing site.

Edi