Cascaded latent thermal storage can find its applications in renewable thermal energies with time dependent temperatures. This paper presents thermal performance of cascaded heat storage with unsteady inlet temperature of heat transfer fluid (HTF). The optimization of temperatures of HTF and phase-change materials (PCMs) is performed based on exergy, entropy, and entransy. Corresponding analytical/numerical solutions with these concepts are obtained. The qualifications for existence of optimization solutions are proposed. The optimization result of unsteady case is compared with that of steady case. The fluctuation of HTF temperature is transferred along the HTF flow path. The HTF temperatures in different stages exhibit similar fluctuating trend, but the fluctuating amplitude is diminished along the HTF flow path. With an increase in stage number, the difference between temperatures of outlet HTF and environment is gradually decreased with obviously improved thermal performance. As NTU increases, thermal performance is gradually increased, but with decreased increasing amplitude. The optimization result with entransy is also compared with that of entropy. The optimal exergy efficiency based on entropy is greater than that based on entransy, while the optimal thermal efficiency based on entransy is superior to that based on entropy. The optimization can be applied to select PCMs for unsteady cascaded thermal storage. (C) 2016 Elsevier Ltd. All rights reserved.