The study of nonlinear problems related to the process of heat transfer in the substance is very important for practice. One of the problems that arise when studying the characteristics of new materials is the problem of simultaneous identification of temperature-dependent thermal conductivity and volumetric heat capacity of substance based on the results of experimental observations of the dynamics of the temperature field in an object. Previously, this problem was considered only in the one-dimensional case. It is desirable that these studies be carried out for a three-dimensional case, since experimental data are collected from three-dimensional objects. In this work, the above-mentioned problem is considered in the three-dimensional case. The consideration is based on the first boundary value problem for a three-dimensional unsteady heat equation. The inverse coefficients problem is reduced to a variational problem. The standard deviation of the calculated temperature field in the sample from its experimental value was chosen as the cost functional. Formulas for calculating the gradient of the cost functional are obtained. The results of the solution of the formulated problem are presented and discussed.