https://www.cdc.gov/lyme/data-research/facts-stats/lyme-dise...
That said, whether it is hotter or cooler doesn't make much of a difference in terms of how you go about your day - you pretty much have to assume you can encounter them regardless.
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.
It impacts the population, but even a couple solid weeks of -20C weather doesn't seem to be enough to eradicate them.
Humans generally aren't vaccinated for Rabies either, unless you are e.g. a veterinarian who might have a higher chance of exposure to it.
I assume a vaccine would try to be multivalent.
That and deer populations need to be significantly culled (along with rodents, the other part of the Lyme / deer tick population cycle).
In any case, lack of long consistent extended cold spells in the winter to set back their breeding population is the reason they've moving further north. Which is tied directly to climate change.