Reuse frying & sauce pans multiple times during cooking session
I think thermal shock is unlikely to be a problem at the temperatures you're likely to use.  I had heard that it is mainly a problem if the pan is very hot (500 degrees or more, although some materials like cast iron are more susceptible to thermal shock than others) and if the shock is very great, like plunging the whole thing into cold water.  

I wouldn't even think about thermal shock at temperatures cool enough to be cooking with - if the water is sizzling and dancing on the pot, that's the test for it being ht enough to cook, and adding room temperature food or liquid for de-glazing are well within the expected ranges for temperature, and probably as much of a temperature difference as you're getting when rinsing your pan.  If your food is done cooking, and cool enough you can put it into plastic without worrying, the pan it's cooked in and that has been off the heat while you're scraping the food out will probably be cooled enough not to crack from being run under water.

As a side note, I once had a pan crack from thermal shock - it did not shatter, or blast pieces everywhere, but spluttered a lot of steam and sharply cracked nearly in half to let it equalize the thermal stress.  It is not pleasant, but it was not quite as terrifying as "blasting pieces" makes it sound.

As for residues, I personally wouldn't worry about them too much - since very little will stay in the pan after being rinsed off, and they should have already been cooked to safe temperatures, the pan doesn't sound like it will be sitting out between sessions long enough to breed anything dangerous (which would be hours), and the next batch of food should be cooked to safe temperatures again.  I would be more concerned about flavor contamination than safety, although different people tolerate different levels of risk.