Is it proper to use an internal layer as a heat bed if I want to warm my multilayer PCB?
I think you could do this. Suggest serpentine tracks that don't form a coil so that the magnetic field won't be especially strong. You can shield electrostatically with a ground plane, but the magnetic field will go right through everything, so if you have sensitive circuits you might need to filter the PWM to something more like DC (not really a big deal, just some inductors and capacitors).  

The copper thickness and resistivity and etching of fine traces are not that well controlled, but +/-20% is not a big deal on a heater (and you might be able to get that repeatably). 

Personally, I'd use a cheap SMT thermistor for the sensor assuming you only want to control at one temperature. Just stick it in and it will work. There will be excitement enough getting the heater to work well.  

Here is an example of a pattern used in a commercial film heater: 



Yours would have to jog around through-holes, but if you splurged on blind vias that could be minimized.