furnace burners wont ignite when furnace room is cold

[BryanM]

My furnace won't cycle when the weather is cold. When the thermostat calls for heat, the pilot lights and burns for 5 seconds then goes out. The thermostat thinks the furnace is heating so doesn't call for heat again and the house gets colder and colder. It used to just happen in the colder months and usually just overnight and simply turning the thermostat off and on again in the morning would fire it up. The problem was intermittent and would work for a few days then the thermostat would have to be turned off and on again. Replaced the thermostat several times over the years. It has gotten worse in terms of not working when the weather is not particularly cold and needing to turn the thermostat (or power to furnace) off and on several times before the burners fire up. I have now paid for 3 service calls to HVAC companies who arrive and turn the furnace off and on again and it fires up so they say nothing is wrong. Something is certainly wrong when my family wakes up every morning to a freezing house and when we all come home after school and work and the house is freezing. Simply turning the thermostat off and on a bunch of times no longer works most of the time and the solution that has been working 100% of the time is to turn on a space heater in the small room where the furnace is for 5-10mins then turn the thermostat on. For some reason the burners won't light after the pilot lights when the furnace is cold but works absolutely fine if the furnace room is warm. Anyone have any ideas as to what component(s) I should start replacing as the HVAC techs that have been here over and over tell me everything is working as It should.  There is no sticker, furnace model or name anywhere on the furnace. All the HVAC techs noted this as well.

[Admin]

What's the model of the furnace?

Intermittent problems like that are usually caused by the ignition module or gas valve.

[BryanM]

The furnace has no markings, labels, stickers or any other identifying marks on it. The techs that have tried to troubleshoot this problem noted the same.

[Admin]

You have to take the doors off and find the rating plate.  It will list the model number.