Warm air blowing on t-stat will cause cycling problems but usually longer duration between cycles.
The short cycling you are experiencing could be due to:
Restricted discharge air flow.......make sure all registers are clear and flowing air
Restricted return air flow.....make sure that return side of furnace is not obstructed
Furnace over-firing due to High propane pressure....pressure should be 11" WC with at least 50% of other propane appliances in service.
High limit switch is faulty.......190*F switch (need to pull furnace to access)
(You can check for 12V fluctuation at connector on circuit board----white wire marked AIR on board. If limit switch is opening/closing power will come/go at that contact)