  The strong form factor of the $B_{c} B_{c}J/\Psi$ vertex is calculated in the
framework of the QCD sum rules method at finite temperature. Taking into
account additional operators appearing at finite temperature, thermal Wilson
expansion is obtained and QCD sum rules are derived. While increasing
temperature, the strong form factor remains unchanged up to $T\simeq100~MeV$
but slightly increases after this point. After $T\simeq160~MeV$, the form
factor suddenly decreases up to $T\simeq170~MeV$. The obtained result of the
coupling constant by fitting the form factor at $Q^2=-m^2_{offshell}$ at $T=0$
is in a very good agreement with the QCD sum rules calculations at vacuum. Our
prediction can be checked in the future experiments.
