The thermal conductivity and heat capacity of single crystals of the spin 1/2 quasi-2D Heisenberg antiferromagnet K(2)V(3)O(8) have been measured from 1.9 to 300 K in magnetic fields from 0 to 8 T. The zero field thermal conductivity data are consistent with resonant scattering of phonons by magnons near the zone boundary. Application of a magnetic field greater than 1 T, however, produces a new magnetic ground state with substantial heat transport by long wavelength magnons.