Integrated circuit-chip hot spot temperatures are reduced by providing localized regions of higher thermal conductivity in the conductive material interface at pre-designed locations by controlling how particles in the thermal paste stack- or pile-up during the pressing or squeezing of excess material from the interface. Nested channels are used to efficiently decrease the thermal resistance in the interface, by both allowing for the thermally conductive material with a higher particle volumetric fill to be used and by creating localized regions of densely packed particles between two surfaces.