[wayner]

Coolant pump is a plastic finned unit. When the fins fail, they will clog the heater core (no more heat) and could clog the cooling galleries in the engine.

IF the thermostat fails, it is an expensive job to get at (or a frustrating one to do yourself)
if that does fail, be sure to do the water pump, which was likely the cause.

In fact, just replace the water pump as preventative maintenance and save yourself all sorts of grief with thermostat, heater core, engine etc.