I uncharacteristically took the time to read my pool heater's manual.
The manual stated that the pool heater has a safety switch that will turn off the heater if the pump is off. I believe it has a pressure switch for this function. The manual indicated that it would be prudent to test the safety feature by turning off the pump while the heater was running. I performed the test, and as soon as the pump was stopped, the heater shut down.