A compressor comprising: a casing; an upstream impeller and a downstream impeller for rotation in the casing; a diaphragm comprised of an internal portion and an external portion; an upstream diffuser fluidly coupled to an outlet of the upstream impeller; a return channel fluidly coupled to the upstream diffuser and to an inlet of the downstream impeller, the return channel has a plurality of return-channel blades connecting the internal and external diaphragm portions; and a downstream diffuser fluidly coupled to an outlet of the downstream impeller is disclosed. A first coolant passage is in the internal diaphragm portion and extends around an inner core, the first coolant passage being in heat-exchange relationship with the upstream diffuser and the return channel. A second coolant passage and third coolant passage are separated by a second inner core in the external diaphragm portion and in a heat-exchange relationship with the return channel and the downstream diffuser.