A cooling apparatus includes first and second wedges, a solid thermal interface material (TIM) and a flexible force-exerting element. The first wedge has a first flat surface and a first diagonal surface. The first flat surface is configured to dissipate heat from an electronic device. The second wedge has a second flat surface and a second diagonal surface. The second diagonal surface faces the first diagonal surface, and the second flat surface is coupled to a heat sink and configured to dissipate heat thereto. The TIM is disposed between the first and second diagonal surfaces, and is configured to transfer heat between the first and second wedges. The force-exerting element is configured to move the first wedge or the second wedge, so as to slide the first diagonal surface or the second diagonal surface on the TIM and push the second flat surface against the heat sink.