An apparatus for transferring heat between two corner surfaces is provided. In one embodiment, an apparatus for transferring heat between two corner surfaces is provided. The apparatus comprises a heat transfer body comprising: a first heat conducting side; a second heat conducting side intersecting with the first heat conducting side to form a corner; and a contact face oriented at an acute angle relative the first and second side. The apparatus further comprises at least one wedge having a slip face oriented at an angle configured to interface with the contact face; and at least one fastener configured to apply a force to the at least one wedge. The wedge is configured to translate the force applied by the fastener into a first component in a direction normal to the first heat conducting side and a second component in a direction normal to the second heat conducting side.