The condenser coils do get hot. They can even be to hot to comfortably touch and this is normal.
The refrigerator should not run constantly.
Running constantly and never cycling off can indicate a cooling problem.
One thing to try is to wait till it has been running a few minutes then open the door and turn your cycling thermostat towards the off position. It should cycle off before getting to the off position on the dial.
If it does not cycle off then it's not getting cold enough to satisfy the thermostat. This is likely the reason the refrigerator runs all the time.
A thermometer in a glass of water can be used to check the temperatures in the refrigerator section.
You can check that all fans are running. If you need additional information then resubmit the question with a model number for the refrigerator.