Where does that "hot fluid in a cold engine" come from? You don't mean the oil or "coolant" do you?
The worst time for the engine is the microseconds while you're cranking it but it hasn't started yet - because oil pressure is low and the rings are scraping what little oil is left on the cylinder walls off. Everything after that is a breeze in comparison, so long as the oil pump is working OK. I pause just long enough for the top to lower or the attractive chimes to stop and then I'm off...