A variable-gap thermal-interface device for transferring heat from a heat source to a heat sink is provided. The device comprises a multi-axis rotary spherical joint comprising a spherically concave surface having a first radius of curvature in slideable contact with a spherically convex surface having the same first radius of curvature. The device further comprises a block having a proximal end rotatably coupled with the heat sink through the rotary spherical joint and having a distal end opposite the proximal end. The device further comprises a wedge having a variable thickness separating a first surface and a second surface opposite and inclined relative to the first surface, such that the first surface is thermally coupled with the distal end of the block, and the second surface is thermally coupled with the heat source.