Heat transfer in a horizontal annular region filled with the viscous fluid is studied experimentally. The external boundary of the working volume is formed by an elastic silicone shell, while the internal one – by a cylindrical copper heater. The walls of the shell are brought into symmetric oscillatory motion by two linear servomotors. The temperature outside the external cylinder is maintained constant by pumping the thermally stabilized liquid. The experiments are conducted with the low heating power that corresponds to relatively low values of the Rayleigh number. This allows maintaining a regime, in which the forced, vibrational convection is the main mechanism of heat transfer. Theoretical analysis of the experimental results shows that the structure of the fluid flows is determined by the competition between the free, thermal convection and the forced one – the steady streaming generated by vibration. At sufficiently high intensity of oscillations, the forced convection dominates and leads to the increase of the heat transfer rate.