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.

My quarterly water/sewer bill is just south of $1200 on the 5 family, heat this month $250.It was built into the rent when I took over and after I implemented conservation/ regulated thermostats and insulation my profit jumped (one heat bill was almost $800, prior to sale).You are set up with separate meters- If you chose to split the bill I would consider whether you can institute cost saving measures first that may give you a profit.

If you use a Nest thermostat for a rental how do you hand off control to a new tenant and terminate control of the old one?

I respect the ethics and definitely agree that it will help to draw an ideal tenant base to you.I'm not sure what your HVAC, plumbing, electrical set up is like in your building, but there are plenty of energy efficient solutions for things like hot water, thermostats, etc.  

I also automate everything, doorlocks, thermostats, cleaning, bill pay etc. good luck

(3) Is it necessary to install a separate thermostat for the AC/heater in the basement?

I believe the thermostats are $50 off right now.