Methods, apparatus and assemblies for enhancing heat transfer in electronic components using a flexible thermal pillow. The flexible thermal pillow has a thermally conductive material sealed between top and bottom conductive layers, with the bottom layer having a flexible reservoir residing on opposing sides of a central portion of the pillow that has a gap. The pillow may have roughened internal surfaces to increase an internal surface area within the pillow for enhanced heat dissipation. In an electronic assembly, the central portion of the pillow resides between a heat sink and heat-generating component for the thermal coupling there-between. During thermal cycling, the flexible reservoir of the pillow expands to retain thermally conductive material extruded from the gap, and then contracts to force such extruded material back into the gap. An external pressure source may contact the pillow for further forcing the extruded thermally conductive material back into the gap.