Stirring of filled polymer systems requires a lot of energy. The mechanical energy converts into heat during the dilatation. In presence of fillers, the heating process takes place not only in the volume of the binder but also near the filler surface so that leads to significant local overheating and change of properties of polymer composition due to the thermal degradation of the filler. As a result, the surface changes occur in the quality parameters of the finished product. Moreover, instrumental methods are almost unable to measure the local temperature of dissipative heating. The transient problem of heat conduction is formulated and solved for the composite system filled with short fibers. The Ostwald – de Waele model is used to describe the rheological properties of the continuum. The axial motion of the fiber in the topological tube is considered. On the surface of the topological tube the boundary condition of Saffman is posed, and on the fiber surface the slip is absent. The velocity profile is found from the flow problem solution. The temperature field is described by the Fourier-Kirchhoff equation taking into account the thermal conductivity in the radial direction as well as the dissipative heat release. The filler and continuum thermal properties are identical and independent on temperature, therefore the conjugate problem can be reduced to the usual problem of transient heat conduction. The solution is obtained in terms of Fourier-Bessel series using Hankel’s integral transform. The numerical analysis for pseudoplastic, dilatant, and Newtonian matrices is performed, and the corresponding evolutions of the temperature field are presented. The “shielding effect” consisting in the slowing of the heating of binding agents in the neighborhood of fibers’ surfaces due to heat sink from the filler is found. The temperature rise for specific process conditions of the stirring of the rubber filled with short fibers is estimated.