We consider here the radial Stefan problem with Gibbs–Thomson law, which is a classical model describing growth or melting of a spherical crystal in a surrounding liquid. We shall specialize to the cases of two and three space dimensions and discuss the asymptotic behaviour of a melting crystal near its dissolution time t* > 0. We prove here that, when the interface shrinks monotonically, the asymptotics near t = t* is of the formHere, R(t) denotes the radius of the crystal, σ is a surface tension parameter and u(r, t) represents the field temperature. An important point to be noticed is that (*) exhibits no dependence on the space dimension N, in sharp contrast with results known for the case σ = 0.