Answer
$$\Delta T = 1.1^{\circ}C$$
Work Step by Step
Using the hint in the problem, we set half the initial potential energy equal to the energy needed to raise the temperature of that mass of iron. Notice that the mass cancels out.
$$\frac{1}{2}mgh = cm \Delta T$$
$$\Delta T = \frac{1}{2c}gh$$
$$\Delta T = \frac{1}{2 (450 J/kg ^{\circ}C)} (9.8 \frac{m}{s^{2}}) (100 m)$$
$$\Delta T = 1.1^{\circ}C$$
