In this paper, an analysis of the temperature condition producing maximal power from a sensible heat source by finite heat-recovery thermodynamic cycles is presented. Some studies have been conducted that theoretically analyzed a system utilizing thermal energy from heat sources by multiple thermodynamic cycles in cascade with the assumption of constant heat-source temperature. However, many heat sources for heat-recovery thermodynamic cycles are sensible, in which the temperature changes considerably with the cycles during heat exchange. Therefore, it is necessary to consider the temperature change of the heat source. First, a temperature condition that maximizes the power generated by a combination of single/multiple Carnot cycles from constant-specific-heat heat sources is analyzed, and the optimal temperature is derived analytically. Subsequently, simulations of the Rankine cycle and several patterns of the Kalina cycle are compared to the analytical model. These comparisons reveal that the Carnot cycle model provides an effective estimation of the temperature conditions for the heat-recovery cycles that produce maximal power from a sensible heat source.