The generation and propagation of thermoacoustic waves in mildly supercritical carbon dioxide are investigated by solving the fully compressible form of the Navier-Stokes equations. Mildly supercritical fluids have high thermal conductivity; however the diffusion of heat in such fluids is very slow. Due to the high compressibility of the mildly supercritical fluids, the boundary layer along any heated surface expands and compresses adiabatically the whole fluid. We investigate these interesting phenomena via a high order numerical scheme. A square enclosure filled with supercritical carbon dioxide is considered as the computational domain. Thermally induced pressure waves are generated by heating the left wall. The thermodynamic properties of the slightly supercritical carbon dioxide are calculated via the NIST Standard Reference Database 12 .