Replaced mercury thermostat w/Honeywell CT87K - doesn't work!

You need a specific thermostat for a Wall Furnace it is a Millivolt Thermostat and not a 24v standard thermostat....usually it will work anyway however if the powerpile (generator produces millivolts from the pilot light) is weak it may not be producing enough...or the Pilot light may be dirty and lazy...won't produce enough millivolts ...or you can have bad or dirty contacts or connections....or a combination of any of the above.....a 24v Thermostat and particularly a non-mercury thermostat has too much resistance in it for a millivolt system....as your Wall Furnace (other than the fan) runs on less than 1 volt