A cooling device includes an inner sleeve with an outer surface, an outer sleeve surrounding the inner sleeve, and two end portions extending between the inner sleeve and the outer sleeve at the ends. The inner sleeve, the outer sleeve and the end portions define a peripheral space. A flow guiding structure defines N channels in the peripheral space for coolant to flow, where N is an integer equal to or greater than 1. Each channel has at least two branches, and N pairs of inlet and outlet corresponding to the N channels. The branches of each channel are in fluid communication with a respective pair of inlet and outlet. Each branch extends over a half circumferential part of the outer surface of the inner sleeve. An electric motor incorporating the cooling device is also provided.