Try a cheap dumb thermostat. Your furnace circuit board may be acting
up. You can pull the thermostat out and jump the white and red to see if
anything happens.
Some furnaces can do so by turning the fan off and on within 1-3 seconds
to increase speed. The Carrier can do 5 speeds by toggling fan on and
off manually. The 6th toggle will go back to the lowest speed.