You should have a constant stream whatever is going on with the thermostat. Changing the impeller is a fairly simple regular maintaince task.
It is a good idea on a new-to-you motor anyway, while you are at it you can change the oil
in the lower unit.
If you want to flush it first, you can run it in a barrel of water first, but I would change the impeller first... If you do not have sufficient cooling
water you may not be able to run it long without doing damage.