A strain wave gearing (1; 1A) with a built-in motor, comprising: a wave gear mechanism; a motor coaxially incorporated in a center portion of the wave gear mechanism; wherein the motor has a motor stator with a cylindrical stator core, and a motor rotor disposed so as to enclose the motor stator; the wave gear mechanism has a wave generator attached to the motor rotor so as to rotate integrally with the motor rotor; the wave generator is disposed so as to enclose the motor rotor; wherein the motor has a motor bracket to which the motor stator is attached; the motor stator has a hollow part; and the motor bracket has a bracket end plate portion exposed to an exterior, and a bracket shaft portion having a distal-end side away from the bracket end plate portion; the bracket end plate portion protrudes in the direction of a center axis from a center portion of the bracket end plate portion and is coaxially inserted into a hollow center portion of the stator core from an open end of the stator core on one axial side of the stator core, wherein the bracket end plate portion has an outer surface on a side opposite to the bracket shaft portion (43 b) in the direction of the center axis; characterised in that the strain wave gearing (1;1A) with the built-in motor is comprising a heat-insulating spacing disposed between the wave gear mechanism and the motor; wherein the heat-insulating spacing is formed between the motor rotor and the wave generator; the strain wave gearing (1;1A) with the built-in motor is comprising a cooling medium circuit that is provided with a shaft-side cooling medium circuit formed in the bracket shaft portion and an end-face-side cooling medium circuit formed along the outer surface of the bracket end plate portion and communicating with the shaft-side cooling medium circuit, wherein the end-face-side cooling medium circuit is provided with a cooling medium inlet channel joined to a cooling medium supply port, and a cooling medium discharge channel joined to a cooling medium discharge port; the shaft-side cooling medium circuit is provided with a first spiraling flow passage communicating at one end of said first spiraling flow passage with the cooling medium inlet channel, and a second spiraling flow passage joined at one end of said second spiraling flow passage to the cooling medium discharge channel; said two flow, first and second, passages (82a, 82b) communicate with one another inside the distal-end side of the bracket shaft portion; the bracket shaft portion is configured from a cylindrical part and from a columnar portion inserted through a hollow part of the cylindrical part; and the shaft-side cooling medium circuit is defined by two spiraling grooves formed between an internal peripheral surface of the cylindrical part and an external peripheral surface of the columnar portion. a wave gear mechanism; a motor coaxially incorporated in a center portion of the wave gear mechanism; wherein the motor has a motor stator with a cylindrical stator core, and a motor rotor disposed so as to enclose the motor stator; the wave gear mechanism has a wave generator attached to the motor rotor so as to rotate integrally with the motor rotor; the wave generator is disposed so as to enclose the motor rotor; wherein the motor has a motor bracket to which the motor stator is attached; the motor stator has a hollow part; and the motor bracket has a bracket end plate portion exposed to an exterior, and a bracket shaft portion having a distal-end side away from the bracket end plate portion; the bracket end plate portion protrudes in the direction of a center axis from a center portion of the bracket end plate portion and is coaxially inserted into a hollow center portion of the stator core from an open end of the stator core on one axial side of the stator core, wherein the bracket end plate portion has an outer surface on a side opposite to the bracket shaft portion (43 b) in the direction of the center axis; characterised in that the strain wave gearing (1;1A) with the built-in motor is comprising a heat-insulating spacing disposed between the wave gear mechanism and the motor; wherein the heat-insulating spacing is formed between the motor rotor and the wave generator; the strain wave gearing (1;1A) with the built-in motor is comprising a cooling medium circuit that is provided with a shaft-side cooling medium circuit formed in the bracket shaft portion and an end-face-side cooling medium circuit formed along the outer surface of the bracket end plate portion and communicating with the shaft-side cooling medium circuit, wherein the end-face-side cooling medium circuit is provided with a cooling medium inlet channel joined to a cooling medium supply port, and a cooling medium discharge channel joined to a cooling medium discharge port; the shaft-side cooling medium circuit is provided with a first spiraling flow passage communicating at one end of said first spiraling flow passage with the cooling medium inlet channel, and a second spiraling flow passage joined at one end of said second spiraling flow passage to the cooling medium discharge channel; said two flow, first and second, passages (82a, 82b) communicate with one another inside the distal-end side of the bracket shaft portion; the bracket shaft portion is configured from a cylindrical part and from a columnar portion inserted through a hollow part of the cylindrical part; and the shaft-side cooling medium circuit is defined by two spiraling grooves formed between an internal peripheral surface of the cylindrical part and an external peripheral surface of the columnar portion.