The crystallization kinetics of transiently heated, nanoscale water films were investigated for 188 K < T < 230 K, where T is the maximum temperature obtained during a heat pulse. The water films, which had thicknesses ranging from approximately 15-30 nm, were adsorbed on a Pt(111) single crystal and heated with ∼10 ns laser pulses, which produced heating and cooling rates of ∼10-10 K/s in the adsorbed water films. Because the ice growth rates have been measured independently, the ice nucleation rates could be determined by modeling the observed crystallization kinetics. The experiments show that the nucleation rate goes through a maximum at T = 216 K ± 4 K, and the rate at the maximum is 10 m s. The maximum nucleation rate reported here for flat, thin water films is consistent with recent measurements of the nucleation rate in nanometer-sized water drops at comparable temperatures. However, the nucleation rate drops rapidly at lower temperatures, which is different from the nearly temperature-independent rates observed for the nanometer-sized drops. At T ∼ 189 K, the nucleation rate for the current experiments is a factor of ∼10 smaller than the rate at the maximum. The nucleation rate also decreases for T > 220 K, but the transiently heated water films are not very sensitive to the smaller nucleation rates at higher temperatures. The crystallization kinetics are consistent with a "classical" nucleation and growth mechanism indicating that there is an energetic barrier for deeply supercooled water to convert to ice.