Abstract: In this paper, a new method based on the heat dissipation ofmicrostructure is proposed to predict the thermal conductivity of thematerial microstructure. This method is shown to be equivalent to the homogenizationmethod both theoretically and numerically. Based on the finite elementdiscretization of the microstructure, the sensitivity analysis for theeffective thermal conductivity is carried out and the topologyoptimization model of the heat-conducting microstructure is built tomaximize the different combinations of effective thermal conductivitycoefficients related to 2D and 3D multiphase materials. The dualoptimization scheme and the quadratic perimeter constraint are used tosolve the problem and to control the checkerboard pattern duringoptimization procedure. Numerical examples show that the design of themicrostructure using the heat dissipation is effective and can providesatisfactory design results with respect to material microstructures.