Abstract A one-dimensional numerical model of smouldering combustion was developed in order to better understand smouldering and accurately predict forced, upwards, self-sustained smouldering for the purposes of treating hydrocarbon-contaminated soil. The role of local thermal non-equilibrium was explored via a new heat transfer correlation obtained specifically for conditions typical of smouldering hydrocarbon-contaminated soil. The model was calibrated to a smouldering experiment and then confidence in the model was gained by independent simulations of additional experiments. The smouldering chemistry was represented by a two-step kinetic mechanism, with the results indicating that this simple framework was sufficient to reproduce the main features of self-sustained smouldering. Local thermal non-equilibrium was demonstrated to be significant in smouldering, with an average normalized temperature difference of 36% between the air and the sand/fuel. Moreover, incorporating the new non-equilibrium correlation provided accurate predictions, particularly in the heat transfer-dominated regions preceding and trailing the front. Results further demonstrated that the most widely used correlation in the literature effectively ensures local thermal equilibrium and such models could not reproduce the experiments.