A solid sphere floats in a liquid at $10\ ^\circ\text{C}$, with $0.980$ of its volume below the surface. The sphere's material has a coefficient of linear expansion of $2.0 \times 10^{-5}\ \text{K}^{-1}$, and the liquid has a coefficient of volume expansion of $9.6 \times 10^{-4}\ \text{K}^{-1}$. The liquid and the sphere are warmed slowly together. Take each volume to grow as $V = V_0(1 + \gamma\Delta T)$, with $\gamma = 3\alpha$ for the solid. At what temperature does the sphere begin to sink?