We have performed Monte Carlo simulation of electron magnetotransport in a GaAs quantum wire at 77 and 300 K. At sufficiently high electric fields, a magnetic field was found to enhance the electron drift velocity significantly by preferentially suppressing backscattering events. Moreover, the field also decreases the electron temperature (suppressing it well below the lattice temperature at 300 K over a wide range of electric field) which reduces Johnson noise. Surprisingly, the electron temperature is lower at a lattice temperature of 300 K than at a lattice temperature of 77 K when a magnetic field is present. All of these have important implications for the transconductance, unity gain frequency and noise margin of quasi-one-dimensional electronic devices such as quantum wire field effect transistors.