What would cause a gas furnace to keep running after the thermostat is turned off

The "4" only indicates which program is currently running. This thermostat does not display furnace error codes.

In a heating system that uses hot wire ignition for natural gas or propane, this behavior may indicate the furnace failed to detect a flame when the cycle starts. You may get warm air briefly, but because the flame detector isn't working, the system shuts down. After a while, it purges any gas and tries again. The controller board in the furnace may have an indicator light that flashes an error code - look for a label on the access panel that describes what it means.

One common cause of this problem is a buildup of contaminants on the flame sense rod (often the same rod that heats red-hot to ignite the gas). Turn off the power to the furnace, wait for it to cool, then inspect the rod. If it has a whitish film on it, clean that off with Scotch-Brite (TM) or similar product (don't use sandpaper). The flame sensor works by measuring a tiny electrical current through the flame. A buildup of combustion products on the sensor blocks this current.

Warning: if you are not absolutely certain about which part is what in the furnace, don;t take any chances, call in a professional. This is a critical gas safety component.

Make sure your air filter is clean. Is the thermostat satisfied? or is the room temp. still below the thermostat setting? When ever you have to turn the power off and then back on to a furnace that usually indicates that the furnaces ignition control locked out. The first thing that I would try is cleaning the flame rod.

The fan normally runs for a few minutes or so after the gas shuts off.

This removes the heat from the furnace and transfers it into the living space instead of just letting it possibly cause overheating of the furnace until it dissipates. If it is a fan that blows outside, that fan also needs to run for a few minutes to clear exhaust gasses from the furnace - to keep them from dissipating into your home.

its likely the outside control unit board its supposed to only kick on gas only when the temp is at freezing..
or
the inside thermostat is not selected for heat pump, open it an look at the jumper / switch.
or just replace the thermostat , then return it saying you couldnt figure it out. :P
there are a lot more variables here after that you cant know how to check.

Sounds like the Thermostat isn't resetting quickly enough.

First, replace the limit. What causes a furnace to cycle frequently would be either a malfunctioning thermostat, a shorted thermostat wire, a bad control or the thermostats heat anticipator is not set right.

Joss sounds like the anticipator setting on thermostat i would replace it with a digital it will be more actturat . The furnace has to go over temp setting to turn off

sounds like the high limits tripped

I'm not a furnace technician. But I have worked on several Coleman trailer furnaces. So keep in mind that my terminology might not be exactly correct. But I think I can help you.

I don't know what model you are running, but most of them run pretty much the same. You have a four basic components to check. Thermostat; Ignition Control Module; Pressure Switch; and which ever of the following that you have (Glow plug, Electronic ignition, Pilot Light).

I'm assuming that you are referring to the blower as the "Rat wheel blower" (round wheel looking thing with fins on it). If my assumption is correct and if the power from the breaker box to the furnace junction box (Probably with a on and off switch on top or side), than when you give it power (from breaker box and turn thermostat up) the fan (not blower) comes on. If it doesn't there is a probably a problem with your Thermostat or Ignition Module. If it does come on and your glow plug or you igniter tries to work. Than yes, you are correct, you have to have gas pressure to let the pressure switch know that there is adequate gas supply pressure (gas- 5 to 7 W.C, propane 11 to 13 W.C). The reason for this is if the Pressure Switch doesn't feel the correct pressure. It thinks you have a leak and won't release gas for ignition. After you turn the gas on. If the furnace doesn't ignite. Make sure the Thermostat is definitely wired properly. Now we are down to one of three problems. If the Glow Plug, Electronic Ignition, or pilot light are working properly. Than we are down one of two problems. The Ignition Module or Pressure Switch. Check pressure on the Pressure Switch. If yuou don't smell gas it is probably OK. But it is best if you use a manometer. I have rarely found Pressure Switches bad. Normally if I get to that step. It is the Ignition Module. The Ignition Module kind of like the brain of the furnace. It is located behind one of your front panels. It will have approximately 10 wires going to it. Some will be going to the Thermostat, some to the Glow plug (Igniter), some to the Pressure Switch, and some going to the blower.

I have probably said more than you need to know. If I did I apologize. But to wrap it up. You were probably correct. You definitely need gas for the blower to kick on. The furnace has to light and heat up before the blower will Start. Not to keep rattling, but to check to see if the blower motor will run. Is to switch the Thermostat from "auto" to "run".

Good Luck

Need more info. Are you saying that when tstat calls for heat then it short cycles. But if you turn it off then back on it runs ok?