Presents a similarity solution for a three-dimensional boundary layer on a heated cone to simulate the water flow past the forward part of an axisymmetric slender body. The numerical solutions of the ordinary differential equations reduced by the similarity transformation are presented in the region near the vertex of the cone. The results indicate that the cross flow grows as the fluid flows downstream for the cone of a half-angle less than 66.25 degrees. For a cone of a half-angle larger than 66.25 degrees, the magnitude of the cross flow is about the same order as that of the axial flow in the neighborhood of the cone vertex and is suppressed by the favorable pressure gradient as the fluid moves downstream. The effect of the temperature-dependent water viscosity has been shown to enhance the favorable pressure gradient effects and to counterbalance the cross-flow effects.