The problem of laser initiation of high explosives in munitions is considered. In this situation, the laser illuminates a small spot on the casing, and lateral thermal transport affects the initiation temperature. We use a variational method to calculate the critical temperature for explosives' initiation as a function of the laser spot size for common high explosives. The effect of the dwelling time of the irradiation is then evaluated. We demonstrate that in typical situations the critical temperature is determined by the dwelling time rather than by the laser spot size.