We have calculated the evolution of a 0.49 Msolar hydrogen deficient white dwarf up to very low effective temperatures. The final model has been obtained by calculating the evolution of a H-deficient star from the extreme horizontal branch (EHB) up to the white dwarf regime, without going through the asymptotic giant branch (AGB). Progenitor stars of this kind are characterized by the lack of thermal pulses, and are known as AGB-manqué. We have found that the white dwarf has observable carbon abundances once it has cooled down 10000 K. These models are representative of white dwarfs of spectral type DQ (helium atmosphere with carbon trace).