In a wall jet over a convex surface (Coanda flow), the mean streamwise velocity profile may be unstable with respect to a centrifugal instability mechanism. Small initial perturbations can therefore grow to finite-amplitude counter-rotating longitudinal vortices (Gört1er vortices). These vortices may also become unstable (secondary instability) and develop increasing distortions in the streamwise direction. Here, a numerical investigation of the secondary instability mechanisms has been carried out using temporal simulations and solving the full Navier-Stokes equations for incompressible flows. Using the temporal model, global flow effects are neglected, thus allowing to focus on local phenomena. Also, by adjusting the downstream extent of the computational domain, the primary 2D instability modes (viscous and inviscid) resulting from the wall jet velocity profile can be selectively suppressed. Different stages of the growth of laminar Görtier vortices in combination with the two-dimensional wall jet profile have been considered as base flows for the investigation of secondary instability. Two secondary modes previously predicted by theory could be observed. The amplification rate of the sinuous mode was found to be predominant at earlier stages of the Görtier vortex growth, whereas the varicose mode dominates the development farther downstream. Furthermore, it was found that the primary instabilities in the streamwise direction can support the amplification of the varicose mode up to large amplitudes. Finally, a comparison was made with previous studies for boundary layer flow over concave wall.