Maybe sell or lease the land if you don't want to put more rentals on it.Use a wifi water heater and thermostats to save on utilities when no one is there.Market your place on Facebook, Vrbo, Craigslist etc to boost your occupancy rate.

He asked me about what the issue might be and I suggested thermostat if it hadn't ever been changed (it hadn't).

He replaced a brand new thermostat that I installed with another one and wired up the thermostat in correctly and disconnect the electric heat and put it on the emergency heat to make the inspector happy. 

You hate to send someone to fix the heat to find out the tenant doesn't know how to change the battery on the thermostat.... but that is the risk you take.