The cooling rate in specific temperature ranges is one of the most important parameters of the thermal cycle in estimation of the possible structural transformations that occur under the action of concentrated energy fluxes. The knowledge of this quantity makes it possible to predict the phase composition of the zones of thermal effect and judge the causes of typical structural changes. For example, the authors of [1] associate the appearance of tempered martensite in the structure of laser-hardened steel with the presumed circumstance that the cooling rate near the equilibrium temperature decreases so much that in the range of the martensitic transformation it becomes even lower than in conventional quenching. In our earlier work [2] we estimated the cooling rates in the martensitic and bainitic ranges in the course of an analysis of the causes of enrichment of steels with retained austenite due to laser hardening. At present a great number of publications have been devoted to computation of the thermal regime of a solid body subjected to surface heating. As a rule, the authors consider the variation of the temperature as a function of the time or the spatial coordinates. Sometimes they analyze the first derivative of the temperature with respect to time. However, its variation is also considered in the same coordinates (cf. [3, 4]). In the problems of metal physics we have to know the cooling rate in specific temperature ranges, i.e., determine its variation as a function of the running temperature. We have created computer software for solving the stated problem. It makes it possible to determine the cumulative time of residence of a material at a given geometrical point above a specific temperature in addition to the rates of temperature variation. This allows us to estimate the austenization time, the time of dissolution of the disperse phase, etc. We can also compute the temperature gradients. STATEMENT OF THE PROBLEM