My suggestions:

The temp alarm doesn't warn you directly about low flow (i.e., give you early warning), it says "engine already too HOT, if it's working. If that was the case, you wouldn't be running the engine for many seconds before the issue of temp would be (sadly) clear. Those alarms give you precious little time to do something -- if it's working.

The other usual alarm possibility is low oil pressure.

I would replace the sensor alarm After checking to see if it has power or the buzzer/horn isn't "shot".