Turn off the furnace and open it for inspection, using your furnace’s manual as a guide.
Look for cracks or rust spots in the metal walls of the combustion chamber and heat exchanger, using a flashlight if necessary. Also, look for sooty discoloration, which might appear if combustion byproducts are passing through barely visible cracks. You might need a mirror to see inaccessible areas.
Install a carbon-monoxide detector nearby, even if you see no cracks. Metal expands when heated, meaning cracks can widen when the furnace is on. A carbon-monoxide detector will help ensure that no cracks are appearing when the metal is heated during typical operation.
Return the furnace to operating condition and monitor its performance. If you can see the flame on your furnace, ensure it's steady when the fan turns on. If it wavers, there might be a hole affecting the air pressure nearby. Another sign of a leak is rapid cycling on and off, although other factors can cause this as well, according to “Principles of Home Inspection: Systems and Standards,” by Carson Dunlop.