You can run an engine
for a surprisingly long time before it overheats to the point of doing damage. Just cranking/starting the engine
, after it had time to cool, to see if it would run and shutting it down, shouldn't be a problem. If the engine stopped because it overheated, seized and broke something serious, you could possibly do damage but the engine should loudly tell you immediately to cease and desist.
If the temp gauge is not working when the engine has run long enough to heat the coolant water
, it's probably not the thermostat. Thermostats pass some water
through even at idle. If there is no coolant, a properly working temp gauge will not show the proper temperature as they need to be immersed in coolant. Eventually will probably indicate an engine in distress
but could be too late by then. I'd suspect you have a sender or gauge issue. 'sailing jazz' has detailed how to trouble shoot the sender/temp gauge.