An exact solution is presented for the temperature distribution and rate of change of phase for a semi-infinite body where the change of phase occurs over a range of temperatures. The surface temperature is instantaneously changed to and held at a temperature different from the phase-change temperature range and the initial temperature. The transient temperature distribution and rate of melting are also determined for a finite slab in which one or two phase changes take place. The slab is initially at a constant temperature and the temperature of one face is instantaneously changed so that a phase change takes place. The other surface of the slab is insulated. An exact closed form solution is presented for the temperature distribution in the newly formed phase and Goodman’s integral technique is used to find the temperature distribution in the initially existing phase.