If the compressor is hot and the fridge isnt cooling then im afraid it a system fault. Its either a poor pumping compressor or a blockage in the system.
For this fault im afraid it isnt a diy repair. You need to get a fridge engineer in as they will need to put there gauges on the pipe work at the back to see what pressure the compressor is pumping at and the level of gas in there.
If its a blockage then they should be able to regas it from there.
Now the cost of this isnt going to be cheap. A regas only is around the £130 mark roughly. But a new compressor fitted is around the £250 so a very expensive repair.
Im afraid unless its under an insurance plan then there not usually worth fix when you get a fault on the system but thats up to yourself.
Sorry its not good news but if you need anymore info just get back to me.