  The paper is concerned with the Cauchy problem for a semi-linear
hyperdissipative heat equation in Besov and Triebel-Lizorkin spaces which is
related to the generalized Gauss-Weierstrass semi-group via Duhamel's
principle. Using caloric smoothing properties of the semi-group we prove
existence and uniqueness of mild and strong solutions which are local in time.
Moreover, we study well-posedness of the problem.
