The Iow-Mach number approximation is considered to be less restrictive than the Boussinesq approximation. The former represents well the flow behavior in enclosures with relatively large temperature difference, and therefore permits a better understanding of thermally driven flows. However, as the flow becomes chaotic or weakly turbulent, it becomes uncertain whether the Iow-Mach number approximation can properly describe the transition behavior of the flow. In the present study, the behavior of transitional thermally driven flow in a two-dimensional (2-D) differentially heated square cavity filled with a gas has been numerically investigated in cases where the temperature difference increases. The exact governing equations, including the equation of state for ideal gas, are used to calculate the initial phase to transition, and the results are compared in detail with those obtained using the Boussinesq-approximated and Iow-Mach number equations. The applicability of these approximated governing equations has been discussed. It turned out that beyond a certain Rayleigh number, even the Iow-Mach number approximation may not always predict the transition behavior of the flow.