A stacked heat-transfer interface structure for dissipating heat from a circuit board is disclosed to include a heat plate affixed to the circuit board, and relatively thinner first heat transfer devices and relatively thicker second heat transfer devices respectively attached to first and second heat generating electronic devices of the circuit board that have different heights for transferring heat from the first and second heat generating electronic devices of the circuit board to the heat plate for dissipation. Each first heat transfer device comprises a first heat-transfer sheet member having a high heat conductivity and a low thermal resistance and bonded to one first heat generating electronic device, an elastically deformable second heat-transfer sheet member having a low heat conductivity and a high thermal resistance and bonded to the heat plate to compensate for height tolerance of the respective first heat generating electronic device, and a heat-transfer block for spreading heat energy from the first heat-transfer sheet member onto the heat plate through the second heat-transfer sheet member.