With the problems of complicated calculation process and lower computational efficiency in topology optimization using the traditional level set method（LSM） of heat conduction structures,parametric level set method（PLSM） is introduced into topology optimization for heat conduction structures.The compactly supported radial basis functions（CS-RBFs） are used to interpolate the initial level set function.The interpolation coefficients of CS-RBFs are proposed as the design variables,dissipation of heat transport potential capacity is adopted as the objective function,and the volume of material is used as the constraint.The topology optimization model for heat conduction structures is thus built.Because the method of moving asymptotes（MMA） is used to update the interpolation coefficients of CS-RBFs,the process of topology optimization for structures is transformed into that of updating interpolation coefficients and the optimal topology is finally obtained.Numerical examples show that the optimal results using PLSM are essentially in agreement with those of LSM optimal results,which illustrates the feasibility and validity of the proposed method.