A thermal management for EMI shielded circuit packs having one or more high-power components, i.e. heat sources. More particularly, a heat transfer device or assembly for EMI shielded circuit packs is provided whereby multiple components (e.g., high-power components) are cooled by individual heat sinks (i.e., each component has its own individual heat sink) which protrude into an external airflow through individual openings in the lid of the EMI shield. Mechanically-compliant, electrically-conductive gaskets are used to seal the base plates of the individual heat sinks against the lid of the EMI shield enclosure. As such, in accordance with the various embodiments, the conductive gaskets establish a compliance layer which accommodates any variation in the heights of the individual components, thereby, allowing optimum thermal contact between the components and their respective heat sinks without compromising the EMI shielding.