In many applications, it is crucial to control the heat transfer rate of impacting drops on a heated plate. When the solid exceeds the so-called Leidenfrost temperature, an impacting drop is prevented from contacting the plate by its own evaporation. But the decrease in the resulting cooling efficiency of the impacting drop is yet not quantitatively understood. Here, we experimentally study the impact of such water drops on smooth heated surfaces of various substances. We demonstrate that, in contrast to previous results for other liquids, water exhibits spray in the vertical direction when impacting sapphire and silicon. We show that this typical spray formation during impact is a result of the local cooling of the plate. This is surprising since these two materials were considered to remain isothermal during the impact of mm-sized droplets. We conclude and explain that the thermal time scale of the system is not solely determined by the thermal properties of the solid, but also by those of the liquid. We also introduce a dimensionless number comparing the thermal time scale and the dynamic time scale with which we can predict the spraying behaviour at impact.