compressor working on and off?

We have a Samsung american fridge freezer (SR-S2028CSS) and the temperature keeps rising until we turn it off then on and the compressor starts up again until it reaches the right temp then it goes off again, temp rises and so on.. We called out an engineer (£85, here 5 mins and said we need a new compressor) but before we remortgage the house to pay for this (!) my husband is wondering if it's not something simpler that is linked to the compressor like the thermal coupling or could it be the thermostat? Any advice gratefully appreciated!