  The thermal conductivity of electron-doped Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$
single crystals is investigated below 200K, with an emphasis on the behavior
near the magnetic and superconducting (T_c) transition temperatures. An
enhancement of the in-plane thermal conductivity $\kappa_{ab}$ is observed
below T_c for all samples, with the greatest enhancement observed near optimal
doping. The observed trends are consistent with the scattering of heat carriers
by low-energy magnetic excitations. Upon entering the superconducting state,
the formation of a spin-gap leads to reduced scattering and an enhancement in
$\kappa(T)$. Similarly, an enhancement of $\kappa$ is observed for
polycrystalline BaFe2As2 below the magnetic transition, and qualitative
differences in $\kappa(T)$ between single crystalline and polycrystalline
BaFe2As2 are utilized to discuss anisotropic scattering. This study highlights
how measuring $\kappa$ near $T_c$ in novel superconductors can be useful as a
means to probe the potential role of spin fluctuations.
