The motion of a solid-liquid interface in a finite one-dimensional medium, subject to a fluctuating boundary temperature, is analyzed. The fluctuations are assumed to be periodic. The solution method involves a semi-analytic approach in which, at any given time, the spatial temperature distributions are represented in infinite series. The effect of the solid, liquid Stefan numbers and the unsteady boundary temperature variation is investigated. The results showed a retrograde motion of the solidification front for large liquid Stefan numbers.