An evaluation is made of the convective thresholds for the onset of parametric instabilities in the electron cyclotron heated Doublet III plasmas when the operating radiofrequency is 60 GHz. For heating at the fundamental frequency, the convection losses are quite strong so that threshold powers much in excess of present-day power inputs are required. At the second harmonic, the process of resonant decay into two short-wavelength electron Bernstein waves offers the minimum threshold power, which is, however, still somewhat higher than the 650 kW being currently applied.