The article presents a numerical study of the large-amplitude, acoustically-driven streaming flow for different frequencies of the acoustic wave and different temperature gradients between hot and cold surfaces. The geometries studied were mainly two-dimensional rectangular resonators of different lengths, but also one three-dimensional rectangular resonator and one long and narrow channel, representative of a typical U-shaped resistance thermometer. The applied numerical model was based on the Navier–Stokes compressible equations, the ideal gas model, and finite volume discretization. The oscillating wall of the considered geometries was modeled as a dynamically moving boundary of the numerical mesh. The length of the resonators was adjusted to one period of the acoustic wave. The research confirmed that baroclinic acoustic streaming flow was largely independent of frequency, and its intensity increased with the temperature gradient between the hot and cold surface. Interestingly, a slight maximum was observed for some oscillation frequencies. In the case of the long and narrow channel, acoustic streaming manifested itself as a long row of counter-rotating vortices that varied slightly along the channel. 3D calculations showed that a three-dimensional pair of streaming vortices had formed in the resonator. Examination of the flow in selected cross-sections showed that the intensity of streaming gradually decreased as it approached the side walls of the resonator creating a quasi-parabolic profile. The future development of the research will focus on fully 3D calculations and precise identification of the influence of the bounding walls on the streaming flow.