First thing; you might be able to check and clean the contacts for pitting and wear, if you can dress them that is great. Thet are calibrated at the factory, they usually use paint on the adjusting screw to lock it in this set position.
Second thing; I would do this readjust to the controller if possible to the temperature control unit after it has stablized in a regular refrigerator matching it against a known accurate temp gauge. Once this corrected by the adjusting screw add a little paint to the threads to lock the screw in position. Next have the controller this time control a relay as only the relay coil current which is rather low will go thru the controllers contacts, let the relay take the motors starting surge current amperage that is what a relay is designed for. A small current coil controlling a high current item like a motor or a heating element. This would be a inductive or as a resistive load on the relay. Relays are rated for these types of loasd.
It is better to have the relay contacts take the high current hammering and pitting loads instead of the contacts in your temp controller. The relay coil current will be in miliamps range vs high amps that cause this contact wear and pitting in the first place. Not only the above problems you will have different temperatures that the controller cotacts open due to pitting and sticking contacts.
With this set up you will have dead on repeating temps all the time with the controller contacts not take a beating and sticking from all the pitting and contact buildup. Years ago I installed a relay to a 240 volt hot tub as the contacts in the temperature controller were pitted and sticking causing the temps to vary by many degrees, over 27*F. After purchasing a new temp control at $137 because the old one was totally sealed preventing dressing the contacts I had the controller control a relay coils current. The relay contacts took the high current arcing plus the hot tub temp was always stable and within 0.1*F when set at 102.5*F. Your body can feel a 0.25*F to 0.5*F degree difference.
This resulted from soaking 45 minutes or longer to having to get out after 2 minutes. A narrow happy zone for a good hot tub soak of 35 minutes to get the full benefit of the tub on the sore body muscles.
You got my point above about ading a relay I hope.