I would like to install a second thermostat on the lower floor of my home. My thinking is that when we have guest staying on the lower floor I could turn the upper floor thermostat off and the lower on and the heater would respond to the temperature on the lower level. Would this arrangement work?
The other issue will be that if the temperature sensor is in the basement, the upper part of the house may get too warm by the time the furnace displaces all of the cold ait in the basement. Remember, warm air RISES, so if your return air resister is not in the basement, it will be a long time before there is enough air exchange to make a difference down there.
What I would do (have done) is to add a baseboard heater as a supplemental system, with its own thermostat in the basement, along with a way to keep the basement air from rising out of the basement (i.e. stairwell door).
I assume you have forced air heating & cooling.
If not this is very simple with baseboard 220v heat. Add a heater or more on a different 220v circuit, connected to a thermostat.
Forced Air, isn't hard, but probably expensive. You will have to isolate the runs to that particular area. Add a flow switching device, that also activates the end device, with its own Thermostat.
Hot water... if you have PEX and open ports on your manifold. Adding a new controller and zone is cake. If it is an iron pipe...just NO.