A low thermal resistance cooler module includes a heat-transfer base member defining a recess and multiple elongated, curved locating grooves, flat heat pipes set in the elongated, curved locating grooves with respective hot interfaces thereof suspending in the recess and respective cold interfaces thereof bonded to the heat-transfer base member, a heat-transfer block fixedly mounted with the hot interfaces of the flat heat pipes in the recess of the heat-transfer base member for transferring waste heat from a heat source of an external circuit board by direct contact, and connection plates respectively connected between the heat-transfer block and the heat-transfer base member.