Can you help me understand what might be the problem

Take the cover off the burner compartment of the furnace. Obtain the make and model of the furnace off the rating plate in the burner compartment and post it here.

Observe the sequence of events that occurs at the furnace when you turn up the thermostat and post that sequence of events in order and in detail.

Yes, please do give the info SP asked for, then let us know what wires you connect, etc, etc, etc. Glad to be of assistance if you are willing to give us enough info to engage our brains.