I used to have the same engine as an auxilliary.
There's no thermostat on the 2-stroke version at this size.
https://www.tohatsu.com/common/owner...0e78c2fe9f.pdf
Service wise, I know you've done the impeller, did you change the gear oil? Use new fibre washers. I'd check the wiring bullet connectors. They oxidise over time, so pull them apart, light sand with sand paper, and reconnect. Lube grease nipples.
I'd also check the fuel filter near the fuel switch. Personally old fuel can cause issues, so drain and refill. Check the sacrificial anode. Often overlooked, pull, wire brush and refit.
Lastly, change the starter rope. Again, often overlooked.