I had a new Tempstar two stage furnace put in last year and they also put in a Honeywell Non - Programmable Digital Thermostat. The old wires were a basic two wire Red and white system so they used them and I have basic heat. I wanted to to make it so the furnace blower turns on just to push air through the vents in the summer and I was wondering if someone could tell me what wire I would have to add as I do not think I need to add all wires as I do not have A/C.

It will be easier for you just to ad a switch on the fan and limit control to jump the blower part our for summer use. You can just use a wall switch and box and some 14 gage wire. Since I am not there it would be impossible to tell you where this control is located in you furnace but usually it located above the gas valve in the upper part below the vestibule.

No if you have a circuit board in your furmace then that is a different story. You can try to jump red to green and that should bring on the fan.