  Neutrinoless double beta decay (0nubb) is one of the most sensitive probes
for physics beyond the Standard Model, providing unique information on the
nature of neutrinos. In this paper we review the status and outlook for
bolometric 0nubb decay searches. We summarize recent advances in background
suppression demonstrated using bolometers with simultaneous readout of heat and
light signals. We simulate several configurations of a future CUORE-like
bolometer array which would utilize these improvements and present the
sensitivity reach of a hypothetical next-generation bolometric 0nubb
experiment. We demonstrate that a bolometric experiment with the isotope mass
of about 1 ton is capable of reaching the sensitivity to the effective Majorana
neutrino mass (|mee|) of order 10-20 meV, thus completely exploring the
so-called inverted neutrino mass hierarchy region. We highlight the main
challenges and identify priorities for an R&D program addressing them.
