Non-isothermal flow through a curved square channel with strong curvature is investigated numerically by using the spectral method and covering a wide range of the Dean number, Dn, 100≤Dn≤6000 for the curvature δ=0.5. A temperature difference is applied across the vertical sidewalls for the Grashof number , where the outer wall is heated and the inner one cooled. After a compressive survey over the parametric ranges, two branches of asymmetric steady solutions with two- and four-vortex solutions are obtained by the Newton-Raphson iteration method. Then, in order to investigate the non-linear behavior of the unsteady solutions, time evolution calculations as well as power spectrum of the solutions are obtained, and it is found that in the unsteady flow undergoes in the scenario “steady → periodic → multi-periodic → chaotic”, if Dn is increased.