= Solution
Let $K_w$ be the water <thermal conductivity>, $L_m$ the <latent heat> of fusion per unit ice mass, and $\rho_i$ the ice density. Define $v_m>0$ as the normal ice-retreat speed that enlarges the cavity. With the water <thermal boundary layer> at $T_s$ on its warm side and $T_m$ at the melting interface, the heat supply per unit interface area is approximately
$$
q_T\simeq K_w\frac{T_s-T_m}{\delta_T}.
$$
The ice is specified to be uniformly at $T_m$, so no leading sensible-heat flux into colder ice must be subtracted. The <Stefan condition> is therefore $\rho_iL_mv_m=q_T$, giving
$$
\boxed{v_m\simeq\frac{K_w(T_s-T_m)}{\rho_iL_m\delta_T},\qquad\delta_T\sim\delta_v.}
$$
Equivalently $K_w=\rho_wc_p\kappa_T$ expresses the heat flux in terms of water <thermal diffusivity>. The imposed temperatures and constant boundary-layer thickness make this melt rate uniform and constant over the wetted interface. Melting adds latent energy demand to the flow; for an isolated finite pulse, maintaining $T_s$ indefinitely would require heat replenishment. The constant-temperature model is consequently an imposed closure, not a prediction of a permanently hot finite water volume.
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