That does sound like a cool down problem.
That is what I am thinking, no loss in mpg's or performance,
I've always have kept the engine running at high idle with AC on while waiting...………….. (After a high speed run before getting to smog place)
That is what I used to do, but both the shops I use that are "no appointment", now tell you to turn the engine off while waiting, not sure if it is a CARB thing or the local ordinance.