The TIP122 can only handle 5A with good heatsinking. Lets say best case when you turn the transistor on you get a VCE of 0.75V. At 2 amps this results in a power dissipation of 1.5W. If you use the TIP122 with the TO-220 package without heatsinking, the junction to ambient thermal resistance is say 63 degrees Celsius per watt. At 25 degrees celsius that results in a junction temperature of 119.5 degrees Celsius. While that is not hot enough to destroy the device it sure will burn the crap out of your finger if you touch it.
You can do this calculation in reverse to determine the max power dissipation of the device to keep it at or below a certain temperature.
Mike