A coil of platinum wire has a resistance of 100.0 Ω at 20 °C…

Step 1. The formula. $R = R_0[1 + \alpha(T - 20)]$. So $\dfrac{R}{R_0} - 1 = \alpha(T - 20)$.

Step 2. The rise. $T - 20 = \dfrac{128.5/100.0 - 1}{3.9 \times 10^{-3}} = \dfrac{0.285}{3.9 \times 10^{-3}} = 73.1\ ^\circ\text{C}$.

Step 3. The temperature. $T = 20 + 73.1 = 93.1\ ^\circ\text{C}$.