Spray cooling is an effective method to remove high heat fluxes from electronic components. To understand the physical mechanisms, this work studies heat transfer rates from single and dual nozzle distilled water sprays on a small heated surface (1.3 mm x 2 mm). Thermal ink jet atomizers generate small droplets, 33 mu m diameter, at known frequencies, leading to controlled spray conditions with a monodisperse stream of droplets interacting with the hot surface. Of particular interest in this work is the dissipated heat flux and its relation to the liquid film thickness, the surface superheat, and the cooling mass flow rate. Experimental results show the heat flux scales to the cooling mass flow rate. In comparison to published spreading-splashing correlations, these experiments indicate that the drops impinge on the liquid film and spread without generating splashing, leading to high-efficiency stable heat transfer. Surface temperatures range from 120 to 140 degrees C. In addition, the liquid film thickness is investigated in relation to the heater superheat and a stable thin film is seen at superheats beyond 20 degrees C. The efficiency of the spray system is inversely related to the film thickness and may be due to ejection of liquid from the surface due to bursting of vapor bubbles.