Abstract: A barbeque grill assembly comprising a grill shell for holding a heating medium such as charcoal or a gas-distribution plenum. The sides of the grill shell support a heat-exchanger grill element above the heating medium, comprising a plurality of slats disposed in a frame and separated by slots, the slats and slots extending across the grill element. The slats are provided with heat conductor fins in contact with the slats and extending vertically downwards into proximity with the heating medium. Each fin has a relatively large surface area exposed to the hot combustion gases that move upwards from the heating medium toward the grill element, such that each fin abstracts heat from the gases and conducts the heat into the grill slats, thereby increasing the amount of heat derived from the combustion gases, increasing the temperature of the grill slats, and thereby increasing the efficiency of the barbeque grill assembly.