We present an astrometric and photometric wide-field study of the Galactic open star cluster M37 (NGC 2099). The studied field was observed with ground-based images covering a region of about four square degrees in the Sloan-like filters ugi. We exploited the Gaia catalogue to calibrate the geometric distortion of the large field mosaics, developing software routines that can be also applied to other wide-field instruments. The data are used to identify the hottest white dwarf (WD) member candidates of M37. Thanks to the Gaia EDR3 exquisite astrometry we identified seven such WD candidates, one of which, besides being a high-probability astrometric member, is the putative central star of a planetary nebula. To our knowledge, this is a unique object in an open cluster, and we have obtained follow-up low-resolution spectra that are used for a qualitative characterization of this young WD. Finally, we publicly release a three-colour atlas and a catalogue of the sources in the field of view, which represents a complement of existing material.