i really can't give you much advice but our furnace kicked out this AM also..we got up to a cold house.we have a one of those new gas furnaces with the plastic vent rather than a real chimney.
instructions for re-lighting on on the access plate.turn off power-turn off gas--wait--turn on power-turn on gas-replace plate-turn up thermostat---furnace comes on...YES--YES--!!
i think when everyones furnace kicks on really cold AM's the gas pressure drops and the furnace safety system turns it off
i also eyeball the generators at the Big Box shop to keep the furnace running if there is a major power loss in the city. about the best i could do would be to bring the old cast iron box stove that was out at our cabin many years ago from the shed and jerry rig a chimney thru a basement window and burn what wood we can scrounge from the river flats.