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The characterization of white dwarf atmospheres is crucial for accuratelyderiving stellar parameters such as effective temperature, mass, and age. Weaim to classify the population of white dwarfs up to 500 pc into hydrogen-richor hydrogen-deficient atmospheres based on Gaia spectra and to derive anaccurate spectral type-temperature distribution of white dwarfs as a functionof the effective temperature for the largest observed unbiased sample of theseobjects. We took advantage of the recent Gaia low-resolution spectra availablefor 76,657 white dwarfs up to 500 pc. We calculated synthetic J-PAS narrow-bandphotometry and fitted the spectral energy distribution of each object withup-to-date models for hydrogen-rich and helium-rich white dwarf atmospheres. Weestimated the probability for a white dwarf to have a hydrogen-rich atmosphereand validated the results using the Montreal White Dwarf Database. Finally,precise effective temperature values were derived for each object using LaPlata evolutionary models. We have successfully classified a total of 65,310white into DAs and non-DAs with an accuracy of 94%. An unbiased subsample ofnearly 34,000 objects was built, from which we computed a precise spectraldistribution spanning an effective temperature range from 5,500 to 40,000 K,while accounting for potential selection effects. Some characteristic featuresof the spectral evolution, such as the deficit of helium-rich stars at T_eff$\approx$35,000-40,000 K and in the range 22,000 < T_eff < 25,000 K, as well asa gradual increase from 18,000K to T_eff $\approx$7,000K, where the non-DAstars percentage reaches its maximum of 41%, followed by a decrease for coolertemperatures, are statistically significant. These findings will provideprecise constraints for the proposed models of spectral evolution.

White dwarf spectral type-temperature distribution from Gaia-DR3 and the Virtual Observatory