Temp alarm question

[wellcraftv20step]

Morning all,yesterday was the topical day in a boat owners life.. I charged my battery ,hooked up the muffs and started my 97 Yamaha 250 ox66 ,she fired and ran beautifully until after the rpm's dropped then I heard the temp alarm going off so I shut her down. Water seemed to be flowing from the pee hole normally. But I always assumed even with a bad pump you'd never know the pump was bad because it's actually under pressure from the muffs ????? I removed both thermostats as I had planed on doing anyway. Out of curiosity I tested both thermostats by suspending them in a pot of water at about 180 degrees. I realize the water was to hot to start with but I noticed one thermostat opened slowly and the other litteraly poped/snapped open .is this an indication that the one thermostat was bad? I'm running out to pick up a new impeller for the lower unit and thermostats.