<p>Consideration has been given to the method of identifying a complex of thermophysical characteristics in the form of the integral specific heat and the thermal conductivity of a combined thermal protective coating from the results of cryogenic drainage cooling of a cryogenic cylindrical vessel onto which a sample of the highly porous heat insulator under study is wound. This problem is solved in an extremum formulation on the basis of minimizing the standard deviation between theoretical and experimental temperature fields where temperature sensors are installed. The pre-studied quantities are represented in the form of their parameterized values multiplied by linear continuous basis functions which take account of their dependence on temperature. Next, the "primal" problem of heat exchange inside the test sample is solved on specifying operating boundary conditions in the form of a nonuniform thermogravitational heat removal to liquid nitrogen that has been selected as the refrigerant, and on the other side, radiant heat influx by convection. The final stage is minimizing the standard error under study by the conjugate direction method as the most accurate gradient method of first-order convergence. To implement it, an analytical expression has been obtained for the descent parameter ensuring a required convergence of the iterative process with a minimum number of iterations.</p>