The application of weak electric fields (<~ 100 V/cm) is found to dramatically enhance the lattice thermal conductivity of the antiferromagnetic (AF) insulator CaMnO(3) over a broad range of temperature about the Neel ordering point (125 K). The effect is coincident with field-induced de-trapping of bound electrons, suggesting that phonon scattering associated with short- and long-ranged AF order is suppressed in the presence of the mobilized charge. This interplay between bound charge and spin-phonon coupling might allow for the reversible control of spin fluctuations using weak external fields.