The performance of the artificial compressibility (AC) version of the characteristic based split (CBS) scheme for the solution of transient free convection in tall cavities is analyzed. A dual time-stepping procedure is used to recover the transient solution. The true transient term is discretized explicitly up to the fourth order of approximation, with consequent possibility to adopt larger true time-steps and to gain in accuracy and computing efficiency. In order to obtain the present results, the novel stability analysis recently developed by the authors for the steady-state AC-CBS scheme is here extended to the transient algorithm. Cavities with three different aspect ratios have been considered: 8:1, 10:1, and 16:1. The obtained results have been compared with the analytical and numerical data available in the literature.