A heat conductive composite sheet comprising (a) a heat softening, heat conductive layer containing a silicone resin and a heat conductive filler, and (b) a heat conductive silicone rubber layer containing a heat conductive filler is ideally suited to use as a heat radiating structure provided between a heat generating electronic component and a heat radiating component such as a heat sink or a circuit board, for the purposes of radiating heat away from the heat generating electronic component and thus cooling it. This heat conductive composite sheet not only offers good thermal conductivity, but if an installed heat conductive member formed from this type of heat conductive composite sheet needs to be removed temporarily to enable the electronic component such as a CPU to be repaired or replaced, the electronic component is not removed together with the heat conductive member.