"we hit some heat in S. Cal and AZ one year, that our air conditioner would not handle, so had to move along to cooler country before we had intended to."
When I was a child we never had air conditioning in the car. Travelling with Mutzie to the cottage, Mum would wrap her in a damp towel, almost swaddle her. The cat loved it, she was not hot and felt very secure. She was never crated, leashed or otherwise secured.
Of course the heat was never in the leagues of Arizona in the summer.