Polymer based composite materials arc extensively being used in semiconductor packaging as thermal interface materials. In the flip-chip technology these materials are used between the chip and the heat spreader and also between the heat spreader and heat sink. The composites generally have a polymer base and highly conducting ceramic particles as fillers. The size of the filler particles affects the thermal boundary resistance between the particles and the matrix, Rb, and hence the overall thermal conductivity of the composite, k. We have modeled the composite using percolation theory to study the dependence of thermal conductivity and percolation threshold on the Biot number. The temperature dependence of Rb and the critical diameter are also studied using the acoustic mismatch model (AMM) for a polyethylene matrix with alumina particles as filler. The size effect of the alumina particles is also modeled at cryogenic temperatures.