  CUORE will be a 1 ton experiment made of about 1000 TeO$_2$ bolometers. It
will probe the neutrinoless double beta decay (0$\nu$DBD) of $^{130}$Te, a tool
to test the neutrino nature and mass. The excellent energy resolution and the
low background of these detectors will make CUORE a leading experiment in this
field, improving the sensitivity to the half-life of 0$\nu$DBD by more than an
order of magnitude. Bolometric detectors, however, are also sensitive to
nuclear recoils and can be used to search for dark matter interactions. In
principle CUORE, thanks to its mass, could look for an annual modulation of the
counting rate at low energies. We developed a trigger and a pulse shape
identification algorithm, that allow to lower the energy threshold down to the
few keV region. We present the preliminary results obtained on an array made of
four CUORE-like crystals, and the prospects for a dark matter search in CUORE.
