I am dragging up old memories here, so there may be other problems. I replaced a number of over temps that were in the terminal box that was held closed by a spring, and most of those were held against the side of the compressor by a flat spring that dogs into said box.
If yours is like that, you may be able to change out the over temp switch. The trick is going to be getting a replacement. That sure is not a big box or hardware store item. Look for a refrigeration parts place or a Grainger.
Best of luck.
Matt