My furnace is running and putting out heat. However, my thermostat temperature is not rising, so my furnace runs continuously. Does anyone know why this would be? Is my honeywell wall unit going bad on me? The thermostat is only about 2 years old and my quietside furnace is only about 2 years old. My house is warm... but the gas bill is going to be pretty high if I don't get this fixed. Any help or suggestions?

If the heat being produced is keeping the house at the temperature you select then your unit is working OK. The home that you live in must have a very high heat loss and yes your heat bill will be big.