Abstract Applying the variable separation method, an exact analytical solution is found for thermal conductivity equation, established based on the modified Fourier’s law with thermal flux relaxation and temperature gradient under Newton’s boundary conditions (BC). An alternative method is proposed for modeling the transient heat conduction in the plate washed at the boundaries by a liquid or gas, which differs from the traditional one in the absence of the need to determine the heat transfer coefficients from the criterial heat transfer equations, instead of which it is proposed to introduce summands into the classical heat conductivity equation. The summands should take into account the relaxation nature of solids, the features of heat transfer at the boundary, acceleration of heat flux and temperature gradient during the process.