A thermostat is basically an on/off switch, so the smarter ones need to have power to them. Those will either use internal batteries, or require power from the HVAC system. The basic thermostat just connects the R terminal to the W terminal like a switch...there is NO return to complete the circuit for power AT the thermostat...all it does it apply power to the HVAC system, the return to complete the circuit is IN the HVAC system.
IF your thermostat requires power to run FROM the HVAC system, then, you'd need the return (called common) run up to the thermostat. There are ways to make it work without running that extra wire or cable (like using a remote 24-vac transformer and an isolation relay), and some thermostats can parasitically pull power off of the line, but not all HVAC systems will like it! I had one that I tried years ago, and it fried my HVAC system. That system used solid state internal controls, and didn't like what the thermostat did to power itself.
If that third wire is to control the fan manually or for control of the A/C system, and you don't have or want to do that, then it should work with just the two wires for simple heating control as an on/off switch.