  We investigate the mass and decay constant of the heavy-heavy pseudoscalar,
$B_c$, $\eta_c$ and $\eta_b$ mesons in the framework of finite temperature QCD
sum rules. The annihilation and scattering parts of spectral density are
calculated in the lowest order of perturbation theory. Taking into account the
additional operators arising at finite temperature, the nonperturbative
corrections are also evaluated. The masses and decay constants remain unchanged
under $T\cong 100 ~MeV$, but after this point, they start to diminish with
increasing the temperature. At critical or deconfinement temperature, the decay
constants reach approximately to 35% of their values in the vacuum, while the
masses are decreased about 7%, 12% and 2% for $B_c$, $\eta_c$ and $\eta_b$
states, respectively. The results at zero temperature are in a good consistency
with the existing experimental values as well as predictions of the other
nonperturbative approaches.
