The installation has a milk collecting reserve connected to a storage tank by a conduit system and equipped with a transfer pump to assure transferring of milk, where the conduit system is equipped with a heat exchanger (10) to assure cooling or pre-cooling of static milk within the heat exchanger. A central tube (5b) is placed within a peripheral tube (12) in a concentric manner. An outer surface (5b2) of the central tube and an inner surface (121) of the peripheral tube define an annular space (15) that allows passage of cooling fluid with respect to flow direction of milk. An independent claim is also included for a heat exchanger for a conduit system of a milk transferring installation.