Man does that sound familure.
Immed solution if you have electric is a space heater or two, However I do not like 1500 watt heaters on RV type outelts save for the washer/dryer outlet if so equipped.. Figure out a 12 gauge way to power them (I installed additional outlets that are of higher quality).
Second... I will append the Furnace Tribble Shoot guide to this but I suspect your control board.. That was my problem when it happened 5 years ago.. I went with a Dionsaur board from American RV in California (there are many American RV's the one in California had the part in stock about half the price of an OEM board and ... I was SERIOUSLY impressed by the quality, I'm an Electronics trained technician and hobbyist so when I say I'm impressed.. It's impressive)
Now for the boiler plate file
This document was created while I was diagnosing MY furnace.. I am told I missed one possible issue... Sadly I forget if I updated the document or not and the issue Bad connections anywhere along the line can lower voltage
When the T-Stat calls for heat the control board starts the blower (1)
The blower blows closing the sail switch (2)
The control board then opens the gas valve (3) and begins sparking (4.1)
Gas Flows (5) And ignitets (4.2)
The flame heats the flame sensor (5)
The flame sensor sends .480 volts to the control board (6)
which then detects the .480 and continues operation (*)
When the T-stat says "Enough already" (RV is now warm)
The control board shuts off the gas flow (*)
and then turns off the blower after a cool down (*)
*: At nearly every step the control board is involved. IF IT IS BAD, things will not work.. I recommend replacement boards from Dinosaur boards.. When Mine went out the Dino board was less than half the price and when opened the box the quality of construction and workmanship, and then design was very clear to my trained eyes.
1: No 12 volt to furnace, blower motor shot
2: Low 12 volt, air ducts clogged, blower "obstructed" bad sail switch
3: Bad solenoid, Clogged Gas Jet
4: .1: Bad ignition circuit (high voltage) on control board. .2: Points too wide (Very common it seems)
5: These do not often fail but they can
5: Bad connection, NOTE:
5 and * Bad wire.
* applies to all steps by the way So does bad wire/connection.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times