Sounds like furnace is short cycling. The most likely cause for this condition is an over temperature condition that is caused by restriction in the air flow, You need to check the intake and discharge air duct work for any restrictions. A faulty over temperature protection device that is operating at a lower temperature.than designed could also cause your problem.
When I purchased my 04 Holiday Rambler I had the same problem, After much frustration finally determined that it was caused by insufficient air flow in the duct work, the air temperature was found to be greater than setting of the over temperature device. Checked back pressure with a water manometer and found back pressure was greater the manufactures specification. Added an additional discharge vent, problem solved.
Jim