Estimating effective thermal damage process coefficients for the first order model of damage processes is not difficult when the temperature is held constant for a substantial period. Laser coagulation experiments, however, are of short duration and, because of non uniform beam profiles, exhibit important heat transfer effects: the thermal histories are transient by nature. We obtain the activation energy, E, and collision frequency factor, A, directly from the transient history at the boundary of the zones of white coagulation and red hemorrhagic coagulation in liver in the rat, as identified in histologic studies. The estimates are obtained by testing a large number of coefficients and determining the "best fit" from a cost function. Useful values may obtained from a single experiment if the transient history used has a very high confidence level N i.e. a few excellent curves are preferable to single curves at a large number of durations of exposure.