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Abstract. Three approximate methods, viz. the Heat Balance Integral method (HBI), the Modified Heat Balance Integral method (MHBI) and the Double Integral Method (DIM) in combination with hybrid profiles (HP consisting of an exponential and polynomial) are evaluated for relative merits in solving the onedimensional heat diffusion equation. Applications to two linear test problems (TP 1 -semi-infinite solid with constant heat flux at its boundary, TP 2 -semi-infinite solid with step change in its surface temperature) yield the HP-MHBI as the most desirable combination. Applications to nonlinear problems show that these combinations are ideally suited for obtaing reliable and accurate appoximate solutions.