Depends on the pot... I have a bunch of cast-iron & carbon-steel pans and most of those would get a hot rinse, and then a wipe with an oily cloth after going back on the element to heat back up & dry off any excess water.

My cheaper saucepans I probably wouldn't bother unless there'd been a mishap and an egg had cracked - but we also have really hard water here so its often a good idea to wash from time to time.