I have a 25 year old Lennox gas hot air furnace with a Honeywell programmable thermostat that's about 15 years old. The furnace hasn't been coming on consistently and the t-stat display is sometimes normal, sometimes blank, and occasionally every icon on the display is lit up. It's time for a new thermostat. I found that I can trick the thermostat to start the furnace by clicking the mode switch to 'off' and then back to heat. The issue is that the furnace goes into cool down mode and then starts back up again by itself. I can hear relays clicking on and off in the existing thermostat when this happens. I have a new thermostat but won't be able to install it for a day or two. My question is: can the furnace safely cycle on and off for long periods of time?