  Within a two-band model for the recently discovered ferropnictide materials,
we calculate the thermal conductivity assuming general superconducting states
of $A_{1g}$ ("s-wave") symmetry, considering both currently popular isotropic
"sign-changing" $s$ states and states with strong anisotropy, including those
which manifest nodes or deep minima of the order parameter. We consider both
intra- and interband disorder scattering effects, and show that in situations
where a low-temperature linear-$T$ exists in the thermal conductivity, it is
not always "universal" as in d-wave superconductors. We discuss the conditions
under which such a term can disappear, as well as how it can be induced by a
magnetic field. We compare our results to several recent experiments.
