I have central air and heating unit in my home. I have the wall thermostat set for 72 degrees. It will come on with warm air for a while, but after a short time it will start blowing cold air. The temperature in my house has dropped as low as 60 degrees and it will still blow cold air. I removed the cover and noticed that when I did that the burners in the furnace would ignite and the warm air returned. I put the cover back on and after a while it would blow cold air again. What is the problem?

Thank You!

It sounds like an air flow problem and the unit is dropping out on limit. Check your filters, make sure they're clean. If they're packed and you don't have another filter, remove the existing and run the furnace to test/provide heat and pick up another filter quickly(within 48 hours).
Check and maker sure your return vents (sucks air into furnace) are all clear and all supplies (hot/cold air blows out) are clear as well. If these two fail to fix it, check the amp draw of the motor with just the fan running-the motor/capacitor may be going bad and not generating enough air flow.
Lastly... check carbon monoxide and look for a breached heat exchanger. On some models/makes if the heat exchanger is breached, it will trip the limit to prevent operation, as the potential for delivering CO through the air stream is present.

I realize this is a wide range of "ifs" but with the limited description, these are the first that come to mind.

Ps... I just reread the post for the 4th time and picked up on "removed the cover"... *what* cover? If you are taking the cover off the burner assembly of a sealed combustion compartment-you have a blocked combustion air intake! If this is a Carrier/Bryant high efficiency with a 2 pipe (2 pvc pipes connected to furnace 2"diameter) disconnect the uppermost pipe from the burner assembly, scoot it back, and clean the leaves out of the intake. This should make the furnace run again. If that solves the problem, cover the intake on the outdoors side with chicken wire or screen to keep debris out of the intake. This will prevent future nuisance service interruptions.