We present measurements of the dissipation and frequency shift in gold nanomechanical resonators at temperatures down to 10 mK. The resonators were fabricated as doubly clamped beams above a GaAs substrate and actuated magnetomotively. Measurements on beams with frequencies 7.95 and 3.87 MHz revealed that from 30 to 500 mK the dissipation increases with temperature as
T
0.5
, with saturation occurring at higher temperatures. The relative frequency shift of the resonators increases logarithmically with temperature up to at least 400 mK. Similarities with the behavior of bulk amorphous solids suggest that the dissipation in our resonators is dominated by two-level systems.