How to install a timer next to thermostat to control/limit the length of time the thermostat operates?
No one would ever do that.   

They would get a programmable thermostat. It is trivial to set up programs that do exactly what you want to do.  Further, many thermostats have mechanical gating so the up and down (temperature) buttons are readily accessible and changeable right now, but will reset at the next program time.  Access to program is gated by a special door.  You can then put a cage over top of it so they can access the buttons, but not the door.  They typically allow 4 program changes per day.  

This is a $50 solution, and you can't homebrew a thing like that for so little.