Donkey milk is nutritionally rich and has low allergenicity; thus, whey protein derived from donkey milk is a suitable hypoallergenic alternative. However, the temperature during pasteurisation considerably influences the structure and processing characteristics of whey proteins. We found that donkey milk has poor thermal stability; the secondary structure of the whey proteins loosened and became disordered as the temperature increased. In addition, exposing tryptophan and tyrosine to an external polar environment changed the tertiary structure. High-temperature and long-duration heat treatments significantly affected the processing properties, such as emulsification, foaming, and rheological properties. However, a short treatment at approximately 85°C improved the processing properties. Therefore, we recommend that donkey milk be processed at temperatures no higher than this temperature to maintain the beneficial qualities of the whey proteins and provide a reference for processing donkey milk products.