He adjusts the thermostat.

Many companies now make Wifi Thermostats, I have one that is actually supplied by the energy company and it has been great.

Got free digital thermostats, door sealing and light bulbs.

Use new screws (probably stainless) on reassembly - chances are good that they're the same as the other inner door panel screws, if you need a sample to take to the hardware store.The original problem may well be the timer, but sometimes the timer deliberately turns off the power to its own motor and waits for another device (like a float switch or a thermostat) to bring the power back. 

Are they able to control the temperature of the radiator heat with the thermostat?

Could a pipe have come loose so that warm air isn't getting to the thermostat area?

They'll set the thermostat at a certain temp and provide them with a nice space heater.

I save $$$ big $$$ every year because my lead tech takes the time to try to walk the resident/tenant through the problem they are having and resolve via phone if possible.My favorite hero call every time, is when it is 20 below and tenant calls with a furnace out issue, turns out it is simply the batteries in the thermostat, many people do not know that the thermostat in nearly all cases (except for a modern nest) are not direct connect/direct wire and are powered via battery.

As long as you set the property up the right way in the beginning (ring camera's, smart locks on the doors, smart thermostat, good cleaning team etc) then it shouldn't be much more work than watching the pricing on your calendar and answering guest questions once the rental is set up.

Easiest way is to have a programmable thermostat that allows you to set minimum and maximum limits.