A numerical study of acoustic streaming in a cylindrical cavity subjected to vibrational action with a small vibration amplitude is performed. The dependence of the streaming character on the intensity of heat exchange with the surrounding medium is studied. A change in the forms of the acoustic streaming vortices is shown for a smooth transition from adiabatic to isothermal boundary conditions, which occurs via variation in the heat transfer coefficient. The values of the dimensionless heat transfer coefficient are determined for which the acoustic streaming pattern is close to the limiting cases corresponding to adiabatic and isothermal boundary conditions. For limiting cases of thermal boundary conditions, comparison with an analytical solution is performed.