  Two neutrino double $\beta$ decay can create irremovable background even in
high energy resolution detectors searching for neutrinoless double $\beta$
decay due to random coincidence of $2\nu2\beta$ events in case of poor time
resolution. Possibilities to suppress this background in cryogenic
scintillating bolometers are discussed. It is shown that the present bolometric
detector technologies enable to control this form of background at the level
required to explore the inverted hierarchy of the neutrino mass pattern,
including the case of bolometers searching for the neutrinoless double $\beta$
decay of $^{100}$Mo, which is characterized by a relatively short two neutrino
double $\beta$ decay half-life.
