The air that leaves the furnace to heat the house is called the supply, and the air that goes back to the furnace after heating the home is called the return. You subtract the return air temperature from the supply air temperature to get the temperature rise. Each furnace has a temperature rise specified by the manufacturer that shows if it’s heating the way it should. It’ll be listed on a nameplate inside the doors of the furnace as a range of temperatures from low to high.
In order to test the temperature rise, you’ll need a probe thermometer and something to make a small hole in the metal. Then you’ll need to figure out where the return and the supply air are. Look for the arrow for airflow on your air filter. The filter should point towards the furnace. The air flowing towards the furnace from behind the filter is the return. If you follow the furnace past the heat exchanger, that’s the supply side. With that information and the range from the nameplate, you’re ready to test.
In order to run the test, you’ll need to let the furnace run for at least 10 minutes to normalize its temperature. Then you’re going to need an access hole in both the return air ductwork and the supply air ductwork. A small drill bit or metal screw should be enough so that you can pass the probe of the thermometer through. If you’ve had your system serviced, chances are the tech already made access holes.
Now it’s time to test the temperature. Stick the thermometer in the return-side hole and wait for the temperature to stop moving. Then record the result. Repeat this process for the supply side. Once you have those numbers, subtract the supply temperature from the return temperature. That's the temperature rise. With that, you can refer back to the temperature rise range to see if your furnace is within the range listed.