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, a thermal Wilson expansion is obtained and QCD sum rules are derived. While increasing the temperature, the strong form factor remains unchanged up to T similar or equal to 100 MeV but slightly increases after this point. After T similar or equal to 160 MeV, the form factor suddenly decreases up to T similar or equal to 170 MeV. The obtained result of the coupling constant by fitting the form factor at Q(2) = -m(offshell)(2) at T = 0 is in a very good agreement with the QCD sum rules calculations in the case of vacuum. Our prediction can be checked in future experiments.