Phone shut down due to overheating.
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Using a Pixel 7a and Android auto through a wired connection the phone shut down after about 45 minutes because of overheating. This was in an open car with an external temp of approx 12 degrees.
In my previous car I was able to mount the phone by an air vent but this is not possible with my present car.
I did remove the phone from its case, and although it didn't shut down it still became very hot.
I seem to recall this being an issue some time ago, it seems not to have been resolved.