  We report on the temperature dependence of the low-frequency electronic noise
in NiO$_x$/Ga$_2$O$_3$ p-n heterojunction diodes. The noise spectral density is
of the 1/f-type near room temperature but shows signatures of Lorentzian
components at elevated temperatures and at higher current levels (f is the
frequency). We observed an intriguing non-monotonic dependence of the noise on
temperature near T = 380$^\circ$ K. The Raman spectroscopy of the device
structure suggests material changes, which results in reduced noise above this
temperature. The normalized noise spectral density in such diodes was
determined to be on the order of 10$^{-14}$ cm$^2$/Hz (f = 10 Hz) at 0.1
A/cm$^2$ current density. In terms of the noise level, NiO$_x$/Ga$_2$O$_3$ p-n
diodes occupy an intermediate position among devices of various designs
implemented with different ultra-wide-band-gap (UWBG) semiconductors. The
obtained results are important for understanding the electronic properties of
the UWBG heterojunctions and contribute to the development of noise
spectroscopy as the quality assessment tool for new electronic materials and
device technologies.
