I've got twin 90's from the 80's VRO models.
Had the same problem with the alarm going off. I check the lot for overheating problems.
Checked the rubber dividers inside the heads the impeler and all.
Shortly after I rebuilt both motors and on the first run the alarm went off again.
I got a temperature stick and stuck it onto the engine to find the temp fine (stick not melting)
I since changed the thermocouple for the alarm and had no issues since.
In your case however, I would do a service definatelly and get those thermostats put back too. Running an engine cold is nearly just as bad as running it hot.
Impelers are always a problem because some people decide to run the boat without water. Most impelers are rubber and get stuck to the pump housing when they dry out. Without water they rip up to buggery.
Water acts as a lubricant for the pump.
I always turn the engine by hand to free up the pump before starting if the enigine has been sitting for a while.
My temperature gauges on the old controls are not accurate either I ended up putting temp sensors in the water hose so I can see what is going on. It is always good to be able to see this while running the engine.