Spray cooling of a hot target is characterized by strong heat flux and fast change of the temperature of the wall interface. The heat flux during spray cooling is determined by the instantaneous substrate temperature, which is illustrated by boiling curves. The variation of the heat flux is especially notable during different thermodynamic regimes: film, transitional and nucleate boiling. In this study transient boiling curves are obtained by measurement of the local and instantaneous heat flux produced by sprays of variable mass flux, drop diameter and impact velocity. These spray parameters are accurately characterized using a phase Doppler instrument and a patternator. The hydrodynamic phenomena of spray impact during various thermodynamic regimes are observed using a high-speed video system. A theoretical model has been developed for heat conduction in the thin expanding thermal boundary layer in the substrate. The theory is able to predict the evolution of the target temperature in time in the film boiling regime. Moreover, a remote asymptotic solution for the heat flux during the fully developed nucleate boiling regime is developed. The theoretical predictions agree very well with the experimental data for a wide range of impact parameters.