Thermal instability during solidification of a pure melt cooled from above was investigated under a linear stability theory by using the propagation theory. The linearized disturbance equations were transformed similarly by using the thermal boundary-layer thickness as the length scaling factor. The onset conditions of buoyancy-driven convection of the melt with temperature- dependent viscosity were obtained numerically. The results showed that the critical thermal Rayleigh number increases with increasing the dimensionless phase-change rate of a solid-liquid interface, while it decreases with increasing the Prandtl number and Stefan number. Also, it was found that the effect of variable viscosity makes the system more stable and a stagnant layer forms beneath the interface at the onset of convection.