Adding fillers to materials of low thermal conductivity has been recognized as an efficient way to increase the thermal conductivity of composite materials. The filler shapes have great impacts on heat conduction in the materials, which can be analyzed by a direct heat conduction problem. However what is the best shape? This study answers this inverse problem by a nonlinear optimization programming technique. The problem is first standardized to the optimization of a nonlinear objective function with nonlinear constraints. Then it is solved by SQP (sequence quadratic nonlinear programming) numerical scheme. The optimum filler shape parameters are obtained. The results are that the best shapes are "I" shapes. Further, the optimization process can be regarded as a filler growth process. Depending on the fillers thermal conductivity and filler volume contents, the finally formed optimum shapes can be classified into three categories: the handicapped dumbbells, the infant less developed "I" shapes, and adult fully developed "I" shapes. Composite materials made of paraffin wax and steel fillers of six shapes are prepared to validate the optimization results. (C) 2012 Elsevier Ltd. All rights reserved.