We use new observations from the Canada-France-Hawaii Telescope to study the white dwarf cooling sequence of the open cluster M37, a cluster that displays an extended main sequence turn-off and, according to a recent photometric analysis, also a spread of initial chemical composition. By taking advantage of a first epoch collected in 1999 with the same telescope, we have been able to calculate proper motions for sources as faint as g ∼ 26 (about ∼ 6 magnitudes fainter than the Gaia limit), allowing us to separate cluster members from field stars. This has enabled us to isolate a sample of the white dwarf population of M37, reaching the end of the cooling sequence (at g ∼ 23.5). The here-derived atlas and calibrated catalogue of the sources in the field of view is publicly released as supplementary on-line material. Finally, we present an exhaustive comparison of the white dwarf luminosity function with theoretical models, which has allowed us to exclude the age-spread scenario as the main responsible for the extended turnoff seen in the cluster colour-magnitude-diagram.