  We present a coherent and detailed Monte Carlo simulation of the population
of hot white dwarfs. We assess the statistical significance of the hot end of
the white dwarf luminosity function and the role played by the bolometric
corrections of hydrogen-rich white dwarfs at high effective temperatures. We
use the most up-to-date stellar evolutionary models and implement a full
description of the observational selection biases to obtain realistic
simulations of the observed white dwarf population. Our theoretical results are
compared with the luminosity function of hot white dwarfs obtained from the
Sloan Digital Sky Survey (SDSS), for both DA and non-DA white dwarfs. We find
that the theoretical results are in excellent agreement with the observational
data for the population of white dwarfs with hydrogen deficient atmospheres
(non-DA white dwarfs). For the population of white dwarfs with hydrogen-rich
atmospheres (white dwarfs of the DA class), our simulations show some
discrepancies with the observations for the brightest luminosity bins. These
discrepancies can be attributed to the way in which the masses of the white
dwarfs contributing to this luminosity bin have been computed, as most of them
have masses smaller than the theoretical lower limit for carbon-oxygen white
dwarfs. We conclude that the way in which the observational luminosity function
of hot white dwarfs is obtained is very sensitive to the particular
implementation of the method used to derive the masses of the sample. We also
provide a revised luminosity function for hot white dwarfs with hydrogen-rich
atmospheres.
