  We discuss the impact of residual nuclear burning in the cooling sequences of
hydrogen-rich DA white dwarfs with very low metallicity progenitors
($Z=0.0001$). These cooling sequences are appropriate for the study of very old
stellar populations. The results presented here are the product of
self-consistent, fully evolutionary calculations. Specifically, we follow the
evolution of white dwarf progenitors from the zero-age main sequence through
all the evolutionary phases, namely the core hydrogen-burning phase, the
helium-burning phase, and the thermally pulsing asymptotic giant branch phase
to the white dwarf stage. This is done for the most relevant range of main
sequence masses, covering the most usual interval of white dwarf masses ---
from $0.53\, M_{\sun}$ to $0.83\, M_{\sun}$. Due to the low metallicity of the
progenitor stars, white dwarfs are born with thicker hydrogen envelopes,
leading to more intense hydrogen burning shells as compared with their solar
metallicity counterparts. We study the phase in which nuclear reactions are
still important and find that nuclear energy sources play a key role during
long periods of time, considerably increasing the cooling times from those
predicted by standard white dwarf models. In particular, we find that for this
metallicity and for white dwarf masses smaller than about $0.6\, M_{\sun}$,
nuclear reactions are the main contributor to the stellar luminosity for
luminosities as low as $\log(L/L_{\sun})\simeq -3.2$. This, in turn, should
have a noticeable impact in the white dwarf luminosity function of
low-metallicity stellar populations.
