The stability of the parallel time-dependent boundary layer adjacent to a suddenly heated Vertical wall is described. The flow is investigated through experiments in water, through direct numerical simulation and also through linear stability analysis. The full numerical simulation of the flow shows that small perturbations to the wall boundary conditions, that are also present in the experimental study, are responsible for triggering the instability. As a result, oscillatory behaviour in the boundary layer is observed well before the transition to a steady two-dimensional flow begins. The properties of the observed oscillations are compared with those predicted by a linear stability analysis of the unsteady boundary layer using a quasi-stationary assumption and also using nonstationary assumptions by the formulation of parabolized stability equations (PSE).