  Electron conduction opacities are one of the main physics inputs for the
calculation of low- and intermediate-mass stellar models, and a critical
question is how to bridge calculations for moderate and strong degeneracy,
which are necessarily performed adopting different methods. The
density-temperature regime at the boundary between moderate and strong
degeneracy is in fact crucial for modelling the helium cores of red giant
branch stars and the hydrogen/helium envelopes of white dwarfs. Prompted by
recently published new, improved calculations of electron thermal
conductivities and opacities for moderate degeneracy, we study different,
physically motivated prescriptions to bridge these new computations with well
established results in the regime of strong degeneracy. We find that these
different prescriptions have a sizable impact on the predicted He-core masses
at the He-flash (up to 0.01$M_{\odot}$ for initial total masses far from the
transition to non-degenerate He-cores, and up to $\sim 0.04M_{\odot}$ for
masses around the transition), the tip of the red giant branch (up to
$\sim$0.1~mag) and the zero age horizontal branch luminosities (up to 0.03~dex
for masses far from the transition, and up to $\sim$0.2~dex around the
transition), and white dwarf cooling times (up to 40-45\% at high luminosities,
and up to $\sim$25\% at low luminosities). Current empirical constraints on the
tip of the red giant branch and the zero age horizontal branch absolute
magnitudes do not allow yet to definitely exclude any of these alternative
options for the conductive opacities. Tests against observations of
slowly-cooling faint WDs in old stellar populations will need to be performed
to see whether they can set some more stringent constraints on how to bridge
calculations of conductive opacities for moderate and strong degeneracy.
