A thermally-conductive interface interposable intermediate a first heat transfer surface and an opposing second heat transfer surface to provide a thermal pathway therebetween. The interface includes a thermally-conductive compound formed into a layer which is conformable between the first and second heat transfer surface. The compound is an admixture of: (a) a polymeric constituent forming a continuous matrix in the layer; and (b) a dispersed constituent forming discrete domains within the matrix, the domains being form-stable at normal room temperature in a first domain phase and conformable between the first and second heat transfer surface in a second domain phase, and the domains having a domain transition temperature above normal room temperature from the first domain phase to the second domain phase. The dispersed constituent may be a fusible, i.e., low temperature melting, metal or metal alloy.