Driving at all with a migraine is going to be far risky than letting the damn AC run, go find somewhere as cool, dark and quiet as you can instead, you've absolutely earned it, @asherwolf.bsky.social !
Highly unlikely to be an issue. People do that all the time, even whilst home! Obviously there’s the electricity cost, a few dollars, depending on your plan.
This might not fit your budget, and I can't recall if you've ever mentioned your Internet reliability, but these let you turn it off (or on) when you are not home (in future): https://sensibo.com/
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Driving at all with a migraine is going to be far risky than letting the damn AC run, go find somewhere as cool, dark and quiet as you can instead, you've absolutely earned it, @asherwolf.bsky.social !