If you need to check how cold your air conditioner is, follow these steps:
Find the nearest supply air duct to your indoor AC unit.
Then take a thermometer, even a refrigerator thermometer, and tape it just inside the door.
Allow your air conditioner to run for about ten minutes before checking and recording the temperature.
After you've taken your measured data, go ahead and test the nearest return air duct to the unit in the same manner.
Allow your air conditioning to run continuously for 10 minutes before reading and recording your results.
After that, subtract the numbers to find the difference between the two temperatures you recorded. This test should tell you if your system is running and cooling correctly.