Saw someone suggest "cooling degree days" (basically the number of days that it's hot enough out that you'd want the AC on) as a proxy for states where it's currently too hot for people to want to be outdoors. It is indeed quite predictive of current COVID spread.
What's also interesting is that if you add temperature to this, higher temps are associated with lower spread (as most research predicts), controlling for other factors. So heat helps, but being outdoors helps, and you don't want it to be so hot that folks do everything inside.
I would not be surprised if a lot of the early research on weather conflated temperature effects vs. indoor/outdoor effects. If you're comparing places in March, then people will be outdoors more often in warmer places. But that's not necessarily true in the summer.
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