The paper presents solving the boundary value problem of stationary thermal conductivity. It deals with the distribution of the temperature field inside an infinite plate with a cylindrical inclusion under boundary conditions of the first and third kind. The solution was found by applying the Weber–Orr transform to the original function, which shows new approaches to solving boundary value problems of thermal conductivity. As a result, the equations were obtained for determining the temperature field of the plate and the heat flux to the cylindrical inclusion containing zero-order Bessel functions. The result obtained allows to solve the problems of determining the thermal resistance of glass elements of electrovacuum devices with rod inclusions in the form of a circular cylinder, as well as in determining the heat flow to an electric cable from a cable duct in case of fire.