First off.....if cooling unit HAD a leak the 'thermal fuse' would trip due to overheating and you would NOT have any DC to fridge
The HOT area should NOT be HOT.....warm YES but NOT Hot.
It is a heater cable embedded and is energized when fridge has DC...no switch on that model.
Gets power at interior lamp switch (hot wire to switch)
HOT means the heater cable is shorted..need to disconnect hot wire at lamp switch that powers the cable (not lamp)
As for cooling issue......
Quit cooling is not much of a description
You mention that the 'element' got hot when DH turned fridge on.
So A/C is working.
Now you need to test cooling unit functions
The thermistor on fins in food compartment senses temp and thermostat controls cooling cycles based on that sensing.
So CUT THE POWER TO HEATER CABLE so it is NOT energized and burning out.
Then unplug thermistor leads on lower circuit board (P2 connector) so thermistor is 'unavailable' which will cause thermostat to allow for continuous cooling
Then turn fridge ON using the A/C Element.
Let it run overnight (at least 12 hrs) and then check freezer temp and food compartment temp
Freezer S/B 10*F or colder and food compartment 40*F or lower
If so thermistor is BAD and cooling unit is good
IF Not.cooling unit is bad
Is it time for your medication or mine?
2007 DODGE 3500 QC SRW 5.9L CTD In-Bed 'quiet gen'
2007 HitchHiker II 32.5 UKTG 2000W Xantex Inverter
US NAVY------USS Decatur DDG31