screwing into fridge

Since your side walls are heating up when it runs, there are cooling coils in the side. The manufacture, or a service tech that works on the same brand, may be able to tell you where the coils are located in the side walls. If you want to use construction adhesive to glue wood to the ref, check that it meets requirements for below freezing weather, frost, etc. Once it is setup, I doubt that you will be able to remove the glue joint without damaging the ref. Good sources are lumber stores, Lowe's, Home depot.

I do not believe that anyone is trying to mislead you, just trying to help you complete your install. As others have said many have done this conversion with good results.