Don't replace the Roundie, its not broken!
Pete, don't replace your Honeywell Roundie thermostat, it's not broken. Those operate with a mercury switch, and the thermostat must be absolutely level to be accurate. Try leveling your thermostat and see if that fixes it. Take off the front cover and there should be a line on the back, just get a small level, hold it up to the line, and loosten the screws, turn the thermostat housing until its level, tighten the screws, and put the cover on and test.
The mercury switch is a glass vile with a drop of mercury in it. The vile is attached to a bi-metal coil. As the temperature changes, the coil expands and contracts, tilting the glass vile left and right. The drop of mercury slides to whichever end of the vile is lower, one end has the electrical contacts in it. When the drop of mercury hits both contacts, it completes the circuit and turns the system on, when the vile tilts the other way, the mercury leaves the contacts and the system shuts off. If the thermostat isn't level, the vile won't be at the right angle, so just level it.
Mercury is dangerous in nature, so don't juust throw away a perfectly good Roundie,
Dave