A heat pump including a two-stage, high speed fluid compressor including a case having a fluid inlet and a compressed fluid outlet and containing a shaft rotatably mounted about a longitudinal axis, a first compression wheel and a second compression wheel mounted back-to-back on the shaft, the first compression wheel forming a first compression stage and the second compression wheel forming a second compression stage, and a motor positioned between the first compression wheel and the second compression wheel and arranged to rotate the shaft. The case includes an inner through housing extending coaxially to the longitudinal axis and inside which is arranged at least the motor, the inner housing having an inner wall arranged to form, with the motor, channels between at least the inner wall and the motor to cool the motor.