When cool, it should read ambient temperature (eg 30 or so).
In flight with max continuous power set, about 650 - 690 deg - lower power settings, lower TOT.
On shutdown, down to about 250, then creeping back up to about 350 or so as the cooling airflow goes away.
After 30 minutes shut down, would be back to under 150 easily.
If you want to start up after only a few minutes shut down, cranking the engine without introducing fuel cools it down quickly, so the procedure there is (from temp about 300, say):
1. Crank, watch TOT. It will drop quite quickly and smoothly (say 5 seconds to get below 150)
2. When TOT below 150, 'crack' the throttle and continue start as normal.