  Vector ($\Upsilon$) and pseudoscalar ($\eta_b$) bottonium ground states are
studied at finite temperature in the framework of thermal Hilbert moment QCD
sum rules. The mass, the onset of perturbative QCD in the complex squared
energy plane, $s_0$, the leptonic decay constant, and the total width are
determined as a function of the temperature. Results in both channels show very
little temperature dependence of the mass and of $s_0$, in line with
expectations. However, the width and the leptonic decay constant exhibit a very
strong $T$-dependence. The former increases with increasing temperature, as in
the case of light- and heavy-light-quark systems, but close to the critical
temperature, $T_c$, and for $T/T_c \simeq 0.9$ it drops dramatically
approaching its value at T=0, as obtained recently in this framework for
charmonium states. The leptonic decay constant is basically a monotonically
increasing function of the temperature, also as obtained in the charmonium
channel . These results are interpreted as the survival of these bottonium
states above $T_c$, in line with lattice QCD results.
