  We introduce and study an extension of the heat equation relevant to
relativistic energy formula involving square root of differential operators. We
furnish exact solutions of corresponding Cauchy (initial) problem using the
operator formalism invoking one-sided L\'{e}vy stable distributions. We note a
natural appearance of Bessel polynomials which allow one the obtention of
closed form solutions for a number of initial conditions. The resulting
relativistic diffusion is slower than the non-relativistic one, although it
still can be termed a normal one. Its detailed statistical characterization is
presented in terms of exact evaluation of arbitrary moments and is compared
with the non-relativistic case.
