The nonlinear diffusion equation corresponds to the diffusion processes which can occur with a finite velocity. A.J. Janavičius proposed nonlinear equation which describes more exactly the diffusion of impurities in Si crystals in many interesting practical applications. The heat transfer in gases is also based on diffusion of gas molecules from hot regions to the coldest ones with a finite velocity by random Brownian motions. In this case the heat transfer can be considered using similar nonlinear thermal diffusivity equation. The approximate analytical solution of this nonlinear equation can be used for the experimental analysis of thermal conductivity coefficients using temperature profiles dependence on different temperatures and pressures in gases.