  In this article, we study certain type of boundary behaviour of positive
solutions of the heat equation on the upper half-space of $\R^{n+1}$. We prove
that the existence of the parabolic limit of a positive solution of the heat
equation at a point in the boundary is equivalent to the existence of the
strong derivative of the boundary measure of the solution at that point.
Moreover, the parabolic limit and the strong derivative are equal.
