As it has only a single compressor, it is possible that it is running, even when the fridge is cold, in an attempt to chill the freezer.
If it is a frost free freezer, there will be channels hidden inside the casing where the frost is supposed to collect, be melted, and run down to the evaporation dish at the back on top of the compressor.
It might not be the problem in your case, but it is extremely common for frost free freezers to go wrong because these channels get choked with frost and ice. Fixing it is an easy DIY job. Sadly it takes a long time to thaw them out and drain away the melted ice, because the channels are not accessible. If you want to try it, pull the machine out so you can see the evaporation dish and the plastic tube that water runs down (it will probably be full of dirt and maybe fungus, so clean it out). empty the fridge and the freezer and unplug it, leave with the doors open, preferably in a warm room, until water stops dripping out inside or outside (this will take at least a day, possibly two). When you are sure all the internal ice is melted and run out, clean and dry it thoroughly inside and out, and verify that the drain tube is not choked e.g. with food particles or mould. The fill it up and turn it on and see if that has cured it. If not, then it may well be the thermostat, and i don't know how to get at yours.