  For the fractional heat equation $\frac{\partial}{\partial t} u(t,x) =
-(-\Delta)^{\frac{\alpha}{2}}u(t,x)+ u(t,x)\dot W(t,x)$ where the covariance
function of the Gaussian noise $\dot W$ is defined by the heat kernel, we
establish Feynman-Kac formulae for both Stratonovich and Skorohod solutions,
along with their respective moments. In particular, we prove that $d<2+\alpha$
is a sufficient and necessary condition for the equation to have a unique
square-integrable mild Skorohod solution. One motivation lies in the occurrence
of this equation in the study of a random walk in random environment which is
generated by a field of independent random walks starting from a Poisson field.
