To improve the strip rolling technology, it is important to know components of the thermal state of both the strip being rolled and the tool used, that is, rolls at each point of different layers of the strip and rolls, in any section of the deformation zone. It was established that for the numerical solution of thermal problems of heat transfer in the strip-roll system described by equations of unsteady heat conduction, the finite difference method is the most effective. For the further numerical solution of the problems of unsteady thermal conductivity of the strip and rolls during hot rolling, the sections of slabs and rolls were divided by a conditional mesh. Energy balance equations with subsequent finite-difference Fourier approximation for possible options of the mesh nodes occurring in solving the two-dimensional problem of unsteady heat conduction.When solving the heat balance problems for both the strip and the rolls, the performed transformations make it possible to switch from solving the nonlinear heat conduction problem to solving the linearized problem. It was also shown that when calculating the thermal state of the active zone in which cyclic temperature changes occur during one revolution, it becomes possible to switch from solving a problem in a cylindrical coordinate system to solving it in a rectangular coordinate system. Transition to solving a one-dimensional strip-roll system greatly simplifies the calculation. The solution of the III boundary-value problem for the roll and comparison of the obtained results with the results of solutions for the strip-roll system enables the theoretical determination of the heat transfer coefficient in the deformation zone.The study results can be used to determine temperature and speed mode of cooling a thin strip during its rolling as well as set tasks for designing special equipment for accelerated cooling in a production stream of strip rolling mills