The top portion in the "cold" area is the evaportator, the compressor & condensor coil in on the lower deck below,
if the condensor's cooling fan ( electric motor) isn't turning, then..yes, it will get very hot!, so it's time to replace it. usually less than $25.00, then if you are going to be cleaning the machine up, it's relatively easy to remove the whole refrigeration unit as a whole from the machine, you must be careful not to bend/kink or break the copper tubing , although it is quite flexible, it doesn't take kindly to being bent repeativly back & forth.
if the units cooling OK, then you just need to clean it up & give it a nice paint job ( semi gloss black on the lower section & compressor) & rewiring is always a good Idea. Many of the suppliers listed with this site & others have the wiring harness for this machine, ( it's looks like a 60's Vendo V-110)
just be sure to copy down the info off of the ID tag on the side of the machine, (if it has one still.)
You just unplug the wiring connector you see in the lower left side, remove the screws that holds the evaporator in the cabinet, remove the bolt that secures the compressor deck to the bottom of the machine, remove the cover that protects the copper lines & wires going to the upper cabinet, then slide it carefully out of the machine,
once you get it out, you can clean, paint, rewire, & replace the condensor fans motor, & as long as you have it out, it's a good idea to replace the other one too ( evaporator fan), then you can have fun working on the rest of the machine!