• Added missing literature references and improved literature review. • Fixed formulas going beyond the column. • Added experimental setup diagram. • Added a graph for comparing numerical results with experimental data. • Compacted part of the article with a proof of convergence, reduced the amount of information for readability. This paper presents a detailed and developed method for finding soil nonlinear thermophysical characteristics. Two-layer container complexes are constructed. The side faces of which are thermally insulated, so that one can use the one dimensional heat equation. In order not to solve the boundary value problem with a contact discontinuity and not to lose the accuracy of the solution method, a temperature sensor was placed at the junction of the two media, and a mixed boundary value problem is solved in each region of the container. In order to provide the initial data for the inverse coefficient problem, two temperature sensors are used: one sensor was placed on the open border of the container and recorded the temperature of the soil at this border, and the second sensor was placed at a short distance from the border, which recorded the air temperature. The measurements were carried out in the time interval (0 , 4 t max). At first, the initial-boundary value problem of nonlinear thermal conductivity equation with temperature dependent coefficients of thermal conductivity, heat capacity, heat transfer and material density is investigated numerically. The nonlinear initial-boundary value problem is solved by the finite difference method. Two types of difference schemes are constructed: linearized and nonlinear. The linearized difference scheme is implemented numerically by the scalar Thomas' method, and the nonlinear difference problem is solved by the Newton's method. Assuming the constancy of all thermophysical parameters, except for the thermal conductivity of the material, on the segment (0 , t max) , the quadratic convergence of Newton's method is proved and the thermal conductivity is calculated, while the solution of the linearized difference problem was taken as the initial approximation for the Newton's method. By freezing all other thermophysical parameters, and using the measured temperatures in the segment (t max , 2 t max) , the coefficient of specific heat of the material is found. Proceeding in a similar way, using the initial data on the segment (2 t max , 3 t max) , the density of the soil is determined. Also, based on the measured initial data on the segment (3 t max , 4 t max) , the heat transfer coefficient is determined. Based on the experimentally measured data, at each time interval, the corresponding functional is minimized using the gradient descent method. The differentiation of a nonlinear difference problem with respect to the desired parameter method is used to find the gradient of the functional. This method allows you to find the functional gradient and the damping coefficient of the gradient descent in an explicit form. In this case, the compilation and solution of the conjugate problem, which is a frequently used method for solving the inverse problems, is not needed. The performed numerical calculations show that for small time intervals the solutions of the linearized difference problem differ little from the solution of the nonlinear difference problem (1 - 3%). And for long periods of time, tens of days or months, the solutions of the two methods differ significantly, sometimes exceeding 20%. In addition, all thermophysical characteristics (8 coefficients) were found for a two-layer container with sand and black soil. Also the dependence of the temperature difference at the boundary between the environment and the soil for the heat transfer coefficient was shown. [ABSTRACT FROM AUTHOR]