Short cycling — the furnace fires, runs a few minutes, shuts down, then starts again — wears out parts fast and leaves rooms cold. Here are the causes, roughly in order of likelihood.
Restricted airflow
Dirty filter, closed vents, or a blocked return. The heat exchanger overheats and the limit switch shuts things down. Check the filter first.
Dirty flame sensor
A coated sensor can't “see” the flame, so the board closes the gas valve within seconds of ignition. A quick cleaning during a furnace tune-up fixes it.
Thermostat location or wiring
A thermostat near a supply vent or in direct sun satisfies too quickly.
Faulty limit switch or pressure switch
Aging switches trip early or stick. Both are inexpensive parts.
Oversized furnace
A furnace too big for the house heats the space so fast it never completes a proper cycle. The fix is a correctly sized replacement — see furnace installation.
Cracked heat exchanger
Less common but serious. If you also notice a rollout switch tripping or soot, shut the furnace down and call for furnace repair immediately.