The dependence of thermally induced spontaneous magnetization reversal on time-dependent cooling protocols was studied. Slower cooling and longer waiting close to the Nèel temperature of the antiferromagnet ($T_N$) enhances the magnetization reversal. Cycling the temperature around $T_N$ leads to a thermal training effect under which the reversal magnitude increases with each cycle. These results suggest that spontaneous magnetization reversal is energetically favored, contrary to our present understanding of positive exchange bias.