Electron heating in an ultracold neutral plasma is modeled using classical molecular dynamics simulations in the presence of an externally applied magnetic field. A sufficiently strong magnetic field is found to reduce disorder induced heating and three body recombination heating of electrons by constraining electron motion, and therefore heating, to the single dimension aligned with the magnetic field. A strong and long-lasting temperature anisotropy develops, and the overall kinetic electron temperature is effectively reduced by a factor of three. These results suggest that experiments may increase the effective electron coupling strength using an applied magnetic field.