There is very clear correlation between the maps (but, this is one point in time -- not enough to be conclusive!).
You can view MayoClinic's map of new cases per 100K by states for the last 2 months as an animation.
The NYT per-capita map shows localities rather than states.
Do recognize that the difference between a temperature of 10F, 0F, -10F might not impact how much time people spend indoors, nor the difference between 60, 70, and 80F, nor between 110F and 120F.