The combustion of a liquid fuel floating on water is a problem of interest because of its potential environmental and safety consequences. When a liquid fuel is burning under these conditions, the presence of the water may cause some particular effects due to heat transfer to the water. If the fuel layer is thin, heat losses to the water may cause quenching of the fuel burning. If the fuel layer is sufficiently thick, it is possible for the heat transferred to the water to induce nucleate boiling of the water and, in turn, splashing of the fuel above, a phenomenon referred to as thin-layer boilover. In this work, a one-dimensional, transient, heat transfer model of a burning liquid fuel floating on water is developed, and applied to predict the temperature histories in the fuel and water layers, and the time for the onset of boilover. The model includes in-depth radiation absorption but neglects convection within the liquid, and assumes that boilover occurs when the temperature at the fuel/water interface reaches a critical value above the water saturation temperature. Experimental measurements previously made by the authors with different multicomponent. and single composition fuels (crude and healing oil, and several parafines) were used to derive the heal flux at the fuel surface, and an average radiation absorption coefficient, which are two parameters needed as input in the model. It is shown that the model correctly predicts, within the uncertainty of the experiments, the influence of the major parameters of the problem, specifically the initial fuel layer thickness, the pool diameter, and fuel boiling point, on the temperature history of the fuel and water and time to the start of boilover. The effect of the fuel boiling point appears to be complex because a change in boiling point is accompanied by a change in burning rate, surface heat flux, in-depth absorption, and viscosity, all affecting the boilover phenomenon. The model represents a significant improvement from the quasi-steady heat conduction models previously developed by the present and other investigators of the boilover phenomenon.