True gdm-26 cools but constantly runs

Hello. I just acquired a true gdm-26. plugged it in and it cools fine. adjusted the temp to 38 degrees and it continued to run even after reaching the correct temp. 3 hours later still running. Should it turn off after a while? Thanks for the help

I cannot find any info on the given model.

I would unplug the unit and disconnect one of the wires at the thermostat.
Tape it if you have to, to prevent it from shorting to the frame etc.
Then plug it in and give it a try. If it stays off then odds are that the thermostat is toast.
The above assumes that the unit uses a 2 wire thermostat to control the temperature.