Do you remember anything else about the story? If you could provide more details, it'd help a lot!
For now, these are the only fics that come to mind and are similar to what you described:
Not Impervious by Oroyukae
Rated: MA
Summary: He was supposed to be the most powerful demon in existence; one that none could best in any situation, at any time. That was not entirely accurate, it would seem. One error in judgment at the most vulnerable of times, and all that he knows lay in jeopardy. Just what would said being be willing to agree to in the direst of circumstances?
^
(Sesshoumaru found Kagome in this one though, and there's a lot of explicit body-warming in it. He'd also been cursed by a sorceress.)
In From the Cold by Aimee Blue
Rated: M
Summary: AU. Kagome is shocked to find someone not quite human lying unconscious in the snow, but that won't stop her from taking them in.
^
(Kagome does find him in the snow but doesn't save him with body heat per se. In this one, he was branded by an unknown enemy.)
