A conformable heat sink interface for an integrated circuit package comprises a mounting plate having a first surface and a deformable membrane having a portion bonded to a second surface of the plate. A cavity is between the second surface of the plate and the deformable membrane. A flowable heat transfer medium is within the cavity. The flowable heat transfer medium has a thermal conductivity of not less than 30 W/m K. The deformable membrane is to conform to a three-dimensional shape of an IC package and the mounting plate has a second surface that is to be adjacent to a heat sink base.