  We explore the phase diagram of neutral quark matter at high baryon density
as a function of the temperature T and the strange quark mass Ms. At T=0, there
is a sharp distinction between the insulating color-flavor locked (CFL) phase,
which occurs where Ms^2/mu < 2 Delta, and the metallic gapless CFL phase, which
occurs at larger Ms^2/mu. Here, mu is the chemical potential for quark number
and Delta is the gap in the CFL phase. We find this distinction blurred at
nonzero T, as the CFL phase undergoes an insulator-to-metal crossover when it
is heated. We present an analytic treatment of this crossover. At higher
temperatures, we map out the phase transition lines at which the gap parameters
Delta_1, Delta_2 and Delta_3 describing ds-pairing, us-pairing and ud-pairing
respectively, go to zero in an NJL model. For small values of Ms^2/mu, we find
that Delta_2 vanishes first, then Delta_1, then Delta_3. We find agreement with
a previous Ginzburg-Landau analysis of the form of these transitions and find
quantitative agreement with results obtained in full QCD at asymptotic density
for ratios of coefficients in the Ginzburg-Landau potential. At larger Ms^2/mu,
we find that Delta_1 vanishes first, then Delta_2, then Delta_3. Hence, we find
a "doubly critical'' point in the (Ms^2/mu,T)-plane at which two lines of
second order phase transitions (Delta_1->0 and Delta_2->0) cross. Because we do
not make any small-Ms approximation, if we choose a relatively strong coupling
leading to large gap parameters, we are able to pursue the analysis of the
phase diagram all the way up to such large values of Ms that there are no
strange quarks present.
