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 congruent to 100 MeV, but after this point, they start to diminish with increasing temperature. At critical or deconfinement temperature, the decay constants reach approximately 35% of their values in 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 good consistency with the existing experimental values as well as predictions of the other nonperturbative approaches.