We generalize the Spitzer and H¿rm [1953> description of electron heat flow to model the effects of the electron velocity distribution power law tails which are frequently observed [Vasyliunas, 1968; Christon et al., 1988; Maksimovic et al., 1997> in astrophysical plasmas. We apply our generalized heat flow model to the problem of electron heat flow in the solar corona, demonstrating that a weak power law tail in the electron velocity distribution can allow heat to flow up a radially directed temperature gradient. ¿ 1999 American Geophysical Union