A device for milking a dairy animal, comprising a teat cup with a teat liner and a disinfection device for disinfecting at any rate at least a part of the teat liner by means of a disinfecting fluid. The disinfection device comprises a heating device for heating the disinfecting fluid, and the disinfection device is suitable for bringing the disinfecting fluid into contact with at any rate at least a part of the teat liner. A control unit is suitable for controlling the disinfection device. The heating device is suitable for heating the disinfecting fluid to such a temperature that the disinfecting fluid has a temperature of at least approximately 95.degree. C. when it is in contact with the teat liner. The control unit is suitable for registering values of at least one control parameter of the disinfection device.