How can I check my hot water heater temperature? Isn't 120 degrees cold?
Your best bet would be an IR or instant read thermometer.  You should test it from the closest faucet to the hot water tank, and make sure to let it run for several minutes first.

If you do use a leave-in meat thermometer, it might take several minutes to get an accurate reading.

Ice water should be close to 0C/32F (and if you add salt, it would get even colder), which I doubt your meat thermometer can measure.

120F might be considered low, but it is also safer.  140F is a pretty typical setting.