Let the final common temperature be $T_f$. According to the principle of calorimetry, assuming no heat loss to the surroundings, the heat lost by the hot body is equal to the heat gained by the cold body. $\int_{T_f}^{100} C(T) dt = \int_{0}^{T_f} C(T) dt$ Since the heat capacity $C(T)$ increases with temperature, the average heat capacity of the hot body (between $T_f$ and $100^{\circ}\text{C}$) is greater than the average heat capacity of the cold body (between $0^{\circ}\text{C}$ and $T_f$). For the two integrals to be equal, the temperature interval for the hot body must be smaller than the temperature interval for the cold body. $(100 - T_f) < (T_f - 0)$ $100 < 2T_f$ $T_f > 50^{\circ}\text{C}$ Thus, the final common temperature will be more than $50^{\circ}\text{C}$.