523i overheating

It sounds like it could just be your thermostat sticking. it regulates the temperature of your coolant by opening and closing allowing coolant to pass through the radiator. at the same time the water pump could have failed and just depending on how the vehicle is being driven the temperature rises and falls back and forth. also there could be a clog in the cooling system. Right off hand it doesn't sound like the head gasket has failed but its always a possibility. usually a thermostat can run around $350; water pump $450; headgasket can be pretty pricey $3000- $5000 depending on if once the head is removed its sent to the machine shop for sublet work or not. (highly recommend if keeping the vehicle) and always remember on an older vehicle if the cylinder head is taken off there are plenty of other things that might have to be replaced just because of the complexity of the job and how many different systems of the engine have to be disassembled