The paper presents a new approximate method of solving nonlinear direct and inverse heat conduction problems. A nonlinear differential operator is resolved into a linear and nonlinear part. The nonlinearity is treated as an inhomogeneity for the linear operator. Next, the method of successive approximations is used. To solve the problem in each iteration the Trefftz functions (harmonic polynomials) are utilized. The approach presented in the paper has been applied to solve a direct and boundary inverse problem (identification of boundary condition). The sensitiveness of the method according to data disturbance has been checked. Crown Copyright (C) 2012 Published by Elsevier Ltd. All rights reserved.