My Carrier 8000 Weathermaker model 58ctx -135 randomly turned itself on and got the house to about 90 degrees, continued to run and refused to turn off. To shut it down, I turned off the gas supply line. It attempts to restart itself about once every three hours. I disconnected the digital control wires at the thermostat in the house. It still continues to attempt to restart (the glow plug and ignition system activate).

Ultimately, I have pulled all the covers off and some interlock switch has now intervened

What would be the cause of a run away heat always on, no stopping it?

Unless there is a stuck relay, you have a short between R and W in the thermostat wires. Here are some manuals: https://dl.dropboxusercontent.com/u/...20Diagrams.zip
You will need a good digital multimeter to diagnose the problem. First, turn off power and disconnect the wires from the thermostat, after marking them. You should have: R (usually red) that supplies the power to be switched, G (green) fan relay, W (white) heat, Y compressor relay, and sometimes C, which is common (only on some electronic thermostats). Then disconnect the wires at the furnace, after marking them. Put the meter on ohms (make sure no wires touch on thermostat wires) and check to see if there is continuity between W and R, or any other wires. If there is, replace the wire set with a new run, or buy and install a new wireless thermostat. If it checks out to be good and it still runs heat with the wires disconnected then you most likely need a new circuit board unless there is a short or ground in the wiring inside the unit. Rats and ants like to chew on wiring.