Honeywell model is RTH2310B with RC, RH, W, Y, C connectors. My old thermostat has a Red wire and a white wire. I do not know where they connect. I do not have any ac in the room if that helps.

Red to rh (if there is a jumper between rh and rc just leave it in. If no jumper, that's just fine too.) White to w. That should have you up and running.