Re: coolant temperature guage
Not 100% sure, but I'd assume that the PCM would toggle the light when it saw the sensor above a certain value. The rapid cooling also fits the scenario of the pump cavitating, once it slows down, the cavitation stops and you actually start moving fluids again. The only thing that doesn't fit the the normal for your situation is the heat, but, depending on how it's piped and what not, it doesn't necessarily negate the possibility of a worn pump.
'Scuse me, while I scrape this Honda outta my treads.