  The possibility of the formation of a condensate of charged spin-0 nuclei
inside white dwarf cores, studied in arXiv:0806.3692 and arXiv:0904.4267, is
pursued further. It has been shown, for cores composed mainly of one element
(Helium or Carbon), that after condensation phonons become massive and the
specific heat drops by about two orders of magnitude. In this note we extend
that analysis by considering the coexistence of the nuclei of both types
(Helium and Carbon), whose condensation points are generically different. An
effective field theory is developed to describe the system when both elements
are condensed. The spectrum of fluctuations of this two component charged
condensate possesses a collective massless mode with $\omega \propto {\bf
k}^2$. Assuming that the fraction of the less abundant element is greater than
about 1/100, the thermal history changes as follows: There is a softer
discontinuity in the average specific heat after the condensation of first
sector, resulting in slower cooling and a milder drop in luminosity function.
The specific heat remains almost constant until the condensation of the second
sector, then starts to declines as $T^{3/2}$.
