Porous fuels have the propensity to self-heat. Self-heating ignition has been a hazard and safety concern in fuel production, transportation, and storage for decades. During the process of self-heating ignition, a hot spot forms in the fuel layer and then spreads as a smouldering fire. The understanding of hot spot and smouldering spread is important for prevention, detection, and mitigation of fires. In this paper, we build a computational model that unifies the simulation of self-heating ignition and smouldering spread by adopting a two-step kinetic scheme obtained from literature. The model is validated against hot plate experiments of coal in both flat and wedge configurations. The comparison shows that the model predicts the minimum ignition temperature (Tig) and transient temperature profiles reasonably well. The simulation results demonstrate that the hot spot originates at the hot plate and then spreads towards the free surface due to oxygen consumption. In the wedge configuration, the simulations show that the height of maximum temperature point decreases with wedge angle, and that the influence of wedge angle can be explained by the heat transfer. This model brings together two combustion phenomena (self-heating ignition and smouldering) that were traditionally studied separately and analyses the transient behaviour of hot spot and smouldering spread in detail. It deepens our understanding of self-heating fire and can help mitigate the hazard.