My furance dose not fire up to get heating - Heating & Cooling

Sounds like you have to replace the thermo coupler. That is the part that ignites the pilot.

Multiple issues that are not related. If the pilot light goes out then the thermocouple might be bad. If the pilot ignites the gas and everything shuts off, it sounds like the over temperature sensors are detecting heat in excess of what is allowed in the firebox. The thermostat issue has nothing to do with this.

Sounds like limit switch issue. Furnace heats up, high temp limit switch opens, fan will stay on. GMP model is older and do not have the codes.
May be over fired, have airflow problem, to cause the limit to open.
Next time before shutting off power, try to find the limit, it has two wires that connect to a 1.5 x 2 inch card mount to the furnace fire wall. tap on it and see if the blower stops. If so replace the limit.

Sounds like a problem with the furances circuit board. With the furance powered off, disconnect the two wires at the circuit boards thermostat terminal strip. These are probably red and white wires connected to the "Y" and "C" thermostat terminal strip on the circuit board. These two wires send 24 volts to the outside A.C. condenser unit when the thermstat is se tinto the cooling mode. With the thermostst in the "off: postion measure across the "Y" & "C" terminals at the furances thermostat terminal strip. If you have voltaged than either the board or thermostst has failed. The next step to determine which has failed is this. Disconnect all the thermostat wires at the furance. To check the heating circuit jumper across the "R" & "W" terminals, the furance should fire off for the heating circuit and run non stop beacause the thermostat is no longer controlling it and is isolated from the furance. Now remove the jumper and jumper across the "R" &"Y" terminals, the blower should run at your furance for the cooling mode and you should have 24 volts across the "Y" & "C" terminals for the outside A.C. condenser compresor contactor.Next check for blower operation by jumpering across the "R" & "G" terminals. If everything checks outs than the thermostst is the problem. Tou may also want to check the control wiring at the thermostts , furance & out side condenser unit. If the wiring has connnected somewhwre between these points or at the terminal connection this may also be bring on the A.C. when the thermostat is in the "off position.

You may need to replace the furances high limit switch. This is located abvove the burrners with the top frot door off. It has two wires going into it. The furance probably was cycling on this switch which automatically resets it self. The thermal dics wears out and starts to trip at lower temperatures. You can temporally jump across the switch and check the furances opreration but do not leave this switch jumperd because it is a safty.

Flame sensor at furance nees to be cleaned. Remove front top cover at furance. Flame sensor is located left of last burner .Remove 1/4inch screw and clean wirh fine steel whole.

Check the pleum high limit switch. Jump this control out and see if the furance runs until the call for heat is satified. Do mot leave the high limit jumperd.

Check and make sure the filter is clean. This sounds like a restriction in the system. If the unit has central cooling make sure ther indoor evaporator coil is clean at the furance.The unit may be cycling the burners on and off at the high heat limit , fan/limit control. You can also eliminate the thermostst from the furance. Turn power off at the furnace and disconnect the wiring from the thermostat. Jumper the red and white wire together. Turn the furnace back on. The furance should run in the heating mode. Try this and see if the problem is still there.

Try cleaning the flame sensor. Its the most common problem on todays furances. You should clean it with a fine grit sandpaper or emery cloth once a year.

sound like high limit switch or high presure switch