A method of transferring heat from a heat source to a heat sink using a variable-gap thermal-interface device is provided. The method comprises providing and rotating a multi-axis rotary spherical joint to an orientation to compensate for misalignment between the heat source and heat sink. The method further comprises providing a shim of thickness sufficient to fill a gap between the heat source and multi-axis rotary spherical joint, and inserting the shim to fill the gap.