We present results from a study of the dissipation in nanomechanical gold resonators. We fabricated a nanomechanical resonator consisting of a gold wire of width 300 nm, thickness 80 nm and length 7.5 μm by etching away the underlying GaAs substrate. At low temperatures the resonator had a fundamental frequency of about 7.95 MHz, in part due to tension arising from differential thermal contraction between the gold beam and the underlying semiconductor substrate. The dissipation in the resonator was measured using the magnetomotive method over the temperature range 1 K to 10 mK. We find that the Q-factor of the resonator increases by more than a factor of four between 600 mK and 10 mK. The dissipation follows a weak power law dependence on temperature, ∝T0.5, from approximately 30 mK to 600 mK.