We present a model of the solar neighbourhood (d < 100 pc) white dwarf (WD) population and show the resulting effective temperature and mass distribution. Our model parameters, in particular the WD cooling time-scale, are constrained by the models of Chabrier et al. The local initial mass function and star formation rate (SFR, per unit volume in the Galactic plane) of Schröder & Pagel are used for the creation of the synthetic stars from which the WDs originate, as well as the above authors' grid of evolutionary tracks. Furthermore, we consider in detail the significant depletion of the older (and cooler) WDs by dilution into the column, as caused by the dynamics of the 'thin disc'. To verify our synthetic sample, especially the WD cooling time-scale, we study the temperature distribution of a small but nearly complete, volume-limited sample of observed WDs, which we characterize by a single and simple indicator R6300: the number ratio of WDs with Teff < 6300 K over those with Teff > 6300 K . After determination of the bias owing to a residual incompleteness with cool WDs, we find a corrected value of R6300 of 0.68 (±0.24) . This is in good agreement with our WD population model: its temperature distribution yields R6300= 0.77 .For a spherical volume around the Sun, with d < 100 pc , our population model suggests a total of about 13 700 WDs (omiting part of the WDs with a binary system origin, an estimated 7 ± 2 per cent of the total count). A subsample, limited to magnitude 19.0 (as expected for the European Space Agency mission Gaia), would contain about 7750 WDs of this population model. With a less deep magnitude limit of B= 16.0 , more typical of current observed WD samples (SN Ia Progenitor surveY; SPY), the number of objects is reduced to only ≈1350. We use this specific synthetic subsample to test the completeness of the prospective SPY WD sample, which (with over 50 per cent of the candidates now observed) is already the largest sample of WDs with high-resolution spectra. We find that within d < 100 pc and for B < 16.0 SPY will deliver a fairly complete (almost 80 per cent) sample.