If so, why didn't they migrate there? I saw a somewhat similar question asked and it said they didn't move south because of abundant food sources in their current climate, however, that thread didn't address whether they knew there was a more comfortable climate to the south.
EDIT: To specify as to a time period, I guess I would be referring to several hundred years ago or more, when native American tribes were still plentiful and dominant in North America.
As an Inuit, i am curious as to why you think a warmer climate is better? Like, why do you think we would have wanted to move even if we knew about a warmer climate?
A related question: I saw a display at the Field Museum about trade between the Inuit and related peoples of Alaska and native Russian peoples and have wondered why the native peoples of Alaska didn't trade for horses/oxen/reindeer. It seems like the ability to plow and drove beasts of burden would have improved their chances in both inter-native warfare and the later conquests by Westerners.
Did Inuit people know there was warmer land to the south? I can say rather conclusively for my area the answer is "yes," and there actually were attempts to settle further south. Inuit navigated deep into the St. Lawrence. The Beothuk on Newfoundland had to constantly fend off incursions by Inuit from Labrador to the north and Mi'kmaq from New Brunswick and Nova Scotia to the south. A few Inuit settlements occupied Newfoundland for a while historically, but these were abandoned and Inuit territory contracted north again as Euroamericans became increasingly populous in the area.