We consider the two dimensional free boundary Stefan problem describing the evolution of a spherically symmetric ice ball $\{r\le \backslash l(t)\}$. We revisit the pioneering analysis of \cite{HeVe} and prove the existence in the radial class of finite time {\it melting} regimes

which respectively correspond to the fundamental {\it stable} melting rate, and a sequence of codimension $k\in N\ast$ excited regimes. Our analysis fully revisits a related construction for the harmonic heat flow in \cite{RS1} by introducing a new and canonical functional framework for the study of type II (i.e. non self similar) blow up. We also show a deep duality between the construction of the melting regimes and the derivation of a discrete sequence of global-in-time {\it freezing} regimes

which correspond respectively to the fundamental {\it stable} freezing rate, and excited regimes which are codimension $k$ stable.