A rotary heat pump, comprising: a rotary drive section including: a rotary shaft; a stationary gear into which the rotary shaft is inserted; a rotor that has a rotor gear formed to have larger diameter dimensions than outside diameter dimensions of the stationary gear and engaged with the stationary gear, and that makes an eccentric rotation as the rotary shaft rotates; a rotary housing formed to be capable of demarcating a radially outward region of the rotor along a peritrochoid curve defined by the eccentric rotation of the rotor; a first side housing that has an insertion hole for inserting the rotary shaft, that covers one end side of the rotary housing, and that fixes the stationary gear; and a second side housing that covers an other end side of the rotary housing; characterized by heat exchange fins provided on an outer surface of the rotary housing in a compression region where a region demarcated by an outer circumferential surface of the rotor and an inner circumferential surface of the rotary housing has a smallest planar area and an expansion region where the region has the largest planar area; and a bypass path that communicates a plurality of the expansion regions with one another, wherein the heat exchange fins include heat absorption fins provided to the expansion region on an upstream side among two of the expansion regions communicated one another by the bypass path, and heat dissipation fins provided to the compression region located right after the expansion region on a downstream side among the expansion regions communicated one another by the bypass path, and a bypass path heat sink is provided on the bypass path. a rotary drive section including: a rotary shaft; a stationary gear into which the rotary shaft is inserted; a rotor that has a rotor gear formed to have larger diameter dimensions than outside diameter dimensions of the stationary gear and engaged with the stationary gear, and that makes an eccentric rotation as the rotary shaft rotates; a rotary housing formed to be capable of demarcating a radially outward region of the rotor along a peritrochoid curve defined by the eccentric rotation of the rotor; a first side housing that has an insertion hole for inserting the rotary shaft, that covers one end side of the rotary housing, and that fixes the stationary gear; and a second side housing that covers an other end side of the rotary housing; characterized by heat exchange fins provided on an outer surface of the rotary housing in a compression region where a region demarcated by an outer circumferential surface of the rotor and an inner circumferential surface of the rotary housing has a smallest planar area and an expansion region where the region has the largest planar area; and a bypass path that communicates a plurality of the expansion regions with one another, wherein the heat exchange fins include heat absorption fins provided to the expansion region on an upstream side among two of the expansion regions communicated one another by the bypass path, and heat dissipation fins provided to the compression region located right after the expansion region on a downstream side among the expansion regions communicated one another by the bypass path, and a bypass path heat sink is provided on the bypass path.