Abstract A new numerical method using “front tracking” finite elements was developed for the solution of multidimensional transient heat and mass transfer diffusion equations during solidification processes in binary alloys or solutions. The method can cope with irregular geometrical morphologies. The use of this method was demonstrated in a study on the effects of transient, short time, temperature fluctuations on the morphology of a planar solid-liquid interface during a transient solidification process. The numerical studies performed for situations in which the solute in front of the interface was thermodynamically supercooled indicate that the short time temperature perturbations cannot alter the planar morphology of the interface. An explanation of this result was presented in terms of the transient heat and mass transfer processes during solidification.