A technique to evaluate the temperature field is developed by extending the scaled boundary finite element method (SBFEM). Firstly, the method for the steady state problem with prescribed side-face uniform temperature is developed, so only the partial boundary of the problem domain is discretized. Secondly, the effect of the heat capacity on the element interior temperature field is taken into account for the transient heat conduction problem. Thirdly, an improved time domain precise integration method is developed for computing the boundary temperature of the SBFE, meanwhile, a finite-difference scheme is adopted to obtain the element interior temperature at different time. Finally, three examples are presented to illustrate feasibility and good accuracy of the proposed methods. (C) 2015 Elsevier Ltd. All rights reserved.