Universal conductance fluctuations in n-type doped InN nanowires are investigated at temperatures down to 0.35 K. The nanowires were grown by molecular beam epitaxy. The effect of the contact resistance is eliminated by performing the measurements in a four-terminal configuration. We find that the decrease in the conductance fluctuation amplitude with temperature is due to small energy transfer phase-breaking processes and thermal broadening. In contrast to measurements in a two-terminal configuration, the symmetry of the conductance under magnetic field reversal is lost.