Cross−field energy transport by electrostatic plasma waves has been studied theoretically and numerically for a plasma near thermal equilibrium. Energy transfer by plasma waves is significant in a high temperature plasma where collisional transport is quite small. For strong magnetic fields (&ohgr;c≳ &ohgr;p), the simulations verify the theoretical prediction that energy transport by plasma waves increases slowly with the magnetic field, and that in the limit of large field magnitudes, wave transport dominates classical collisional transport. Furthermore, in a strong magnetic field the relaxation of the temperature by wave transport may result in an anisotropic velocity distribution. For weak fields (&ohgr;p≳ &ohgr;c), the simulation shows that collisional transport is more important than wave transport, also in agreement with the theory.