This report describes the research performed during the period March 1987 July 1988 under a joint research program between the Mechanical Engineering Department of the University of Maryland and the Center for Fire Research of the National Bureau of Standards. The research is conducted in the laboratories of the CFR by a Graduate Research Assistant of the ME Department under the joint supervision of Dr. Marino di Marzo (ME Dept. -UMCP) and of Dr. David D. Evans (CFR-NBS). The formulation of a model for the prediction of the cooling induced by an evaporating droplet impinging a semi-infinite solid is the subject of this report. The thermal interactions during the evaporation of a liquid droplet deposited on a low conductivity semi-infinite solid are complex because the evaporative process is coupled to the solid intense local cooling. Numerical techniques based on finite difference methods have failed to provide meaningful results. Preliminary results will also illustrate its validity. A brief note on the convective heat transfer coefficient measured in the previous experiments on aluminum and Macor is also included in this report.