An effective evolutionary method for solving the structural topology design problems of heat conductive fields is presented in this paper. The topology optimization model based on minimizing the heat transport potential capacity dissipation of heat conductive field is then established and the corresponding sensitivity of objective function is derived to determine which elements would be removed of the heat conductive field for having the increment of the objective heat transport potential capacity dissipation minimized. A Filtering technique is employed in sensitivity field to eliminate numerical instabilities in the evolutionary procedure. Numerical examples are presented to demonstrate the validity and the engineering applicability of the evolutionary method by contrast with SIMP method, meanwhile we can come to a conclusion that higher speed of convergence and clearer optimal topology distribution without intermediate elements can be attained by using evolutionary strategy, with the results laying a reliable foundation for the subsequent shape and size optimizations in thermal engineering.