The contact melting problem of a phase-change matrial is studied theoretically. The phase-change material rotating with a constant speed is put a wall which is kept at a constant temperature higher than the melting point of the phase-change material. The problem is governed by four parameters, the Stefan number, the Prandtl number, the ratio of the centrifugal force to the externally applied force, and the ratio of the viscous dissipation to the externally applied heat. The fluid motion and the heat transfer in the narrow gap between the solid and the wall is examined by obtaining an approximate solution expanded in the form of the power series of the Stefan number with the precision up to the first order. It is found from order of magnitude analysis that the melting is caused by the heat transfer from the heated wall rather than the heat generation due to the viscous dissipation, that is, the latter is not important from a point of view of the heat transfer. However, since the attractive force due to the rotation easily exceeds the externally applied force in many practical cases, the effect of the convection on the melting speed is not always found to be negligible, and it causes the liquid-solid interface to be flatter.