This paper presents a numerical scheme for the solution of unsteady velocity and temperature fields in an enclosed compressible fluid that is subjected to thermally induced mechanical motion. The numerical scheme includes revisions of earlier models as well as a scheme applied to the simplified form of the governing equations. The results are compared with previous numerical results and available analytical solutions. The fluid unsteady temperature profile is also compared with recent experimental results. The suggested numerical revisions are shown to improve the results significantly, as verified by experimental data.