This article presents an application of higher order time integration schemes in the dual reciprocity boundary element analysis of nonlinear transient diffusion problems involving nonlinear boundary conditions as well as temperature-dependent material properties. Multistep θ-methods, cubic Hermitian schemes and one-step least squares method have been considered. An error estimate based on the conservation of thermal energy has been presented to assess the accuracy of the numerical solutions. Numerical results are presented for a set of representative test problems to demonstrate the usefulness of the presented time integration algorithms.