Grace of Dragons by Maggie Hoopis:
 
A blizzard is blowing into the Old West.

With the help of a Slewja, a gentle dragon, thirty-three-year-old debutante Grace flees an arranged marriage to Dimin, an older, power-hungry expansionist. When Grace arrives in the dusty frontier settlement of Grogtown she realizes that Dimin injured her with a cold curse and she must continually find sources of heat to remain alive. To combat the curse, she becomes a prostitute, a steady source of inner heat, and learns to embrace the value of independence she never experienced as a society woman.

Grace accidentally alerts Dimin she is alive by ending up on a Wanted poster, and must enter the unknown desert to the west to escape him. She’s joined by two friends and Slewja to evade the quick-tempered Dimin and the cold sickness that he spreads where he goes. Through her adventure, she meets the steadfast dragon rancher, Ignacio, who quickly challenges her beliefs about independence and love.

Will Grace find a way to break her curse before Dimin’s quest for power consumes them all?