We bought a Honeywell thermostat with four wires and our current Mears model has 3 wires colored black, red, and white. The wires on the Honeywell model are 2 red and 2 black. How, if possible, can we use this thermostat with the current wiring?

Do you have AC? Its common to jumper the two reds together. This may help Thermostat wiring colors and furnace terminal designations repair. (http://toad.net/~jsmeenen/wiring.html)