How long will a fridge hold its temperature in a power cut?

That will depend on the temperature outside; whether it is winter or summer, and whether it is opened during the power cut. In winter, at an average temperature of 15ºC in the kitchen, food will be cool for 3 to 4 hours, then they will start to get warmer. In summer, food will not be cool for long. Answer
The time will also depend on the contents of the fridge the more stuff that is in the fridge the longer it will stay at a save temperature. If the freezer compartment (evaporator) is located inside the fridge and it is full of frozen content it can go on for at least 12 hours. I would think things would be okay for at least a day if you keep the door closed, or at least minimize the number of times you open it. Most of the items in your fridge have a lot of water in them, and it takes a lot of energy to warm up water. Plus your fridge is insulated for efficiency reasons, so it's designed not to let in much heat.