White dwarfs (WDs) are the most promising captors of dark matter (DM) particles in the crests that are expected to build up in the cores of dense stellar clusters. The DM particles could reach sufficient densities in WD cores to liberate energy through self-annihilation. The extinction associated with our Galactic Centre makes it impossible to detect the potential-associated luminosities, contrary to smaller stellar systems which are close enough to us and not heavily extincted, such as -Cen. We investigate the prospects of detection of DM-burning WDs in a stellar cluster harbouring an intermediate-mass black hole (IMBH), which leads to higher densities of DM at the centre. We calculate the capture rate and estimate the luminosity that a WD would emit depending on its distance to the centre of the cluster. Direct-summation N-body simulations of -Cen yield a non-negligible number of WDs in the range of radii of interest. We apply our assumption to published Hubble Space Telescope/Advanced Camera for Surveys observations of stars in the centre of -Cen and, although we are not able to identify any evident candidate, we proof that their bunching up at high luminosities would be unique. We predict that DM burning will lead to a truncation of the cooling sequence at the faint end. The detection of DM burning in future observations of dense stellar clusters could allow us to probe different models of DM distributions and characteristics. On the other hand, if DM-burning WDs really exist, their number and properties could give hints to the existence of IMBHs.