  We have computed the masses and decay constants of isotriplet
  $\pi_2(1670)$, the isoscalar $\eta_2(1645)$ and $\eta_2(1870)$ states as the
ground-state nonet of $1^1D_2$ case within the Thermal QCD sum rules framework.
This method is applied to the spectral changes of pseudotensor mesons at high
temperatures including quark, gluon, and mixed condensates up to the five
dimensions. We found that their masses and decay constants are insensitive to
temperature in low-temperature regions. At the near-critical temperature, we
observed an exponential decrease of the masses of $\pi_2$, $\eta_2(1645)$, and
$\eta_2(1870)$, but while the decay constant of $\pi_2$ is fallen, that of
$\eta_2(1645)$ and $\eta_2(1870)$ is increased as a function of temperature.
The modification of condensates at $T\neq 0$ is crucial to the change of
considered mesons properties in a hot medium. We discuss and interpret the
implications of the physical meaning of our results.
