  CUORE is a tonne-scale cryogenic detector operating at the Laboratori
Nazionali del Gran Sasso (LNGS) that uses tellurium dioxide bolometers to
search for neutrinoless double-beta decay of $^{130}$Te. CUORE is also suitable
to search for low energy rare events such as solar axions or WIMP scattering,
thanks to its ultra-low background and large target mass. However, to conduct
such sensitive searches requires improving the energy threshold to 10 keV. In
this paper, we describe the analysis techniques developed for the low energy
analysis of CUORE-like detectors, using the data acquired from November 2013 to
March 2015 by CUORE-0, a single-tower prototype designed to validate the
assembly procedure and new cleaning techniques of CUORE. We explain the energy
threshold optimization, continuous monitoring of the trigger efficiency, data
and event selection, and energy calibration at low energies in detail. We also
present the low energy background spectrum of CUORE-0 below 60keV. Finally, we
report the sensitivity of CUORE to WIMP annual modulation using the CUORE-0
energy threshold and background, as well as an estimate of the uncertainty on
the nuclear quenching factor from nuclear recoils in CUORE-0.
