Hello and welcome to the LOC.
The fan belt or serpentine belt only drives the alternator, AC compressor and power steering pump with an auto tensioner and idler also in the loop.
The water pump is driven off the cambelt so this would not be affected and the engine cooling is controlled by electric fans behind the radiator so no overheating would have occured.
Unless the belt failed due to age you will need to see if anything in the belt's routing has caused it to shred like a worn or out of alignment pulley but any decent garage will be able to check this and advise accordingly.