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.
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