  An active discrimination of the dominant $\alpha$-background is the
prerequisite for future neutrinoless double-beta decay experiments based on
TeO$_{2}$ bolometers. We investigate such $\alpha$-particle rejection in
cryogenic TeO$_{2}$ bolometers by the detection of Cherenkov light. For a setup
consisting of a massive TeO$_{2}$ crystal (285 g) and a separate cryogenic
light detector, both using transition edge sensors as temperature sensors
operated at around 10 mK, we obtain an event-by-event identification of
e/$\gamma$- and $\alpha$-events. We find in the energy interval ranging from
2400 keV to 2800 keV and covering the Q-value of the neutrinoless double-beta
decay of $^{130}$Te a separation of the means of the two populations of 3.7
times their width.
