Thermoacoustic engines use waste heat available at a higher temperature to produce mechanical energy in the form of waves. The purpose of this study is to visualize the fluid behavior downstream of the stack of a thermoacoustic engine by applying numerical analysis and to explore the effect of vortex shedding on the temperature field. The self-sustained oscillation is reproduced by two-dimensional numerical analysis using the compressible solver of OpenFOAM, and the vorticity field and temperature field were visualized. The vortex downstream of the stack changed from symmetric to asymmetric near the peak of the flow velocity. Changes in the vortex structure by the unsteady flow caused irregular and non-uniform temperature field. It is found that the vortex significantly affects the heat transfer between the heat exchanger and the fluid.