The dynamics of a stably and thermally stratified, two dimensional fluid-filled cavity are the subject of numerical study. When gravity is orthogonal to the endwalls, a closed form for a steady state solution with trivial flow may be obtained. However, as soon as the cavity is tilted the flow becomes nontrivial. Previous studies have investigated when this tilt angle is 180 degrees (Rayleigh-Bénard convection), 90 degrees, and 0 degrees, or have done a sweep while solving the steady-state equations. When buoyancy is sufficiently weak the flow is stable and steady up to 90 degrees of tilt. Above a certain level of buoyancy, as measured by the temperature difference between the top and bottom walls, the flow becomes unsteady above a tilt angle less than 90 degrees. Specifically, In this study we examine the relationship between the critical tilt angle and the buoyancy level at the onset of unsteadiness, as well as the dynamical mechanisms by which it occurs.