The present paper is concerned with combustion of an initially spherical kernel of cold fuel, which in a hot oxidizing atmosphere is suddenly put into motion. The investigations are within the framework of an axisymmetric geometry and the flame-sheet model. After a brief description of the acrodynamics of the burning process, including deformation and breakup of the fuel kernel, attention is focused on the study of the combustion time t'(comb), which by definition is the time required to consume practically all the fuel. First, the case of zero heat release is addressed. It is found that - due to deformation and straining of isoscalar surfaces - the direct dependence of the combustion time on the magnitude of the diffusivity of heat and matter decreases rapidly as the Reynolds number, Re, is increased. In particular, the combustion time t'(comb) becomes independent of the magnitude of the diffusivity as soon as the Reynolds number exceeds a few hundred. In this high-Re regime, t'(comb) is found to be proportional to the convective time t'(comb) multiplied by the square root of the density ratio, Eq. 17. Next, the influence of heat release on the combustion time is studied. It is found that at high Reynolds number the combustion time increases with increasing heat release. This increases is found to be essentially due to the decrease of the scalar gradients, which in turn is caused by the gas expansion due to heat release. Furthermore, the effect of heat release on the vorticity distribution is studied, and the relative importance of baroclinicity and gas expansion on the vorticity production is assessed. Finally, the influence of the stoichiometry of the reaction on the combustion time is briefly discussed.