Abstract: An electric machine with a stator, a rotor, and a fluid cooling device. The rotor is supported by a rotor shaft and a first bearing arranged at a bearing shield. The fluid cooling device has a cooling tube secured to a carrier element in fluidic communication with a fluid input and output and extends inside a recess of the rotor shaft while forming an annular space. A sealing element is provided between the rotor shaft and the carrier element, which prevents fluid passage into a spatial region of the electric machine outside of the sealing region. A second bearing is axially spaced apart from the first bearing is between the rotor shaft and a second bearing shield for supporting the rotor. The rotor core extends in a space between the first bearing and second bearing, and the recess extends inside the rotor shaft axially to the second bearing.