Starting with the traditional time‐invariant parabolic‐cylinder model to represent the growth of a platelet‐shaped crystal in a pure supercooled melt, the effect of thermal imbalance at the solid‐liquid interface is calculated. In particular, the heat field equations are solved for the initial excess velocity distribution at the interface, on the assumption that the shape constraint is suddenly replaced by the constraint of heat conservation. The computed results resemble those found for the paraboloidal needle crystal. In particular, the hypothetical parabolic interface tends to bulge with a pronounced peak at one radius behind the leading edge of the platelet crystal. The maximum velocity principle, when applied to this model, yields a square‐law relation between the dimensionless tip velocity and the supercooling for pure ice and water. The results parallel those calculated by Horvay and Cahn for the isothermal model. The curvature effect of surface tension and the effect of the molecular attachment kinetics are found to lower the dimensionless tip velocity by about 20% below that in the isothermal model, uniformly over the range of supercooling considered.