Loose connection!
Try removing the cover to the thermostat. Connect the two wires together. The furnace should start immediately and then produce heat. Separate the two wires, the furnace will go into cool down mode and shut off.
The small bi-metal thermostats can act like what is happening. Look at the contacts for pitting. Could use emery board to clean them up. Temporary fix!
A battery powered electronic thermostat is a good replacement.
Bud
USAF Retired
Pace Arrow
2003 Chev Ice Road Tracker