It's the length and depth of cold days in the winter that can potentially limit their breeding populations, is my understanding. So the issue is that more northerly areas are getting much more variance in temperature and lacking long deep consistent cold periods.

Up and down cycles in temperature have always been a thing on the North American continent but climate change has made it even more variable. We will still get places where it gets very very cold but not for the consistent chunks of time it takes to set back tick populations significantly.

TLDR I don't think it's the heat or cold per se but the variance.

And yes climate change is absolutely the prime factor in their spread. Into places where they were not ever a threat before.