Sorry, it wasn't too clear in your statement, so I check to make sure .
The compressor is running and getting hot, there is no cooling inside the appliance.
This is either no refrigerant in the appliance (leak), faulty compressor (running but not pumping) or a blockage in the system pipework.
I'm afraid none of these are diy repairs.
You would need to have a refrigeration engineer attach gauges and a vacuum pump to the compressor pipework to determine the exact cause.
If it's blocked or leaking, it may not be repairable.
If it is repairable, you'll have the labour charge and the cost of a regas.
If it's the compressor at fault, you'll need a new compressor and regas to get the machine running again.
Unfortunately, these are expensive repairs.
A compressor and regas (depending on the compressor) would cost between £150 and £200. (some compressors push the price to nearer £300)
Sorry, not the news you were hoping for nor an easy fix.
Hope this helps