An arrangement for cooling an electrical machine is provided. The electrical machine is connected with a first cooling-system which directly cools the electrical machine. The first cooling-system circulates a first cooling-medium. The first cooling-system is connected with a second cooling-system which delivers heat from the first cooling-system to the second cooling-system. The second cooling-system circulates a second cooling-medium to remove the received heat. The first cooling-system is connected with a third cooling-system, which is a refrigeration-system, to additionally cool down the first cooling-medium of the first cooling-system.