A heat sink assembly for mounting an LED module to a surrounding main heat sink member is disclosed. The heat sink assembly has a first plate with inner and outer faces and a peripheral edge. The assembly further includes a second plate that is movable with respect to the first plate and has inner and outer faces and an inwardly-tapered peripheral camming surface. Also included in the assembly is an expandable ring sandwiched between the first and second plates. The ring has an inward peripheral edge that engages the camming surface and an outward heat-transfer surface. The ring is expandable beyond the peripheries of the first and second plates. The heat sink assembly also has a sandwiching-device that adjustably interconnects the first and second plates such that sandwiching of the ring facilitates heat-transfer engagement of the heat-transfer surface with the main heat sink member.