A circuit card clamp (300) including a base member (316), at least one first wedge member (446), and a thermally conductive membrane (350). The base member has an elongated shape configured for insertion in a circuit card chassis slot (106). The first wedge member is movable relative to the base member in response to a first actuator (304) for engaging the circuit card chassis slot. The thermally conductive membrane is coupled to the base member and the first wedge member. The thermally conductive membrane has slack for permitting the first wedge member to move relative to the base member between a first clamped position and a second unclamped position. The thermally conductive membrane defines a thermal conductive path (206) between a circuit card (104) and the chassis slot for releasably securing a circuit card in the circuit card chassis slot.