Using the Lagrangian function, the Hamiltonian of the inductance coupling mesoscopic circuits is given. The Hamiltonian operator is diagonalized by introducing a unitary operator. By virtue of the generalized Hellmann-Feynman theorem, the quantum fluctuations of charge and its conjugate quantity for the system at finite temperature are investigated. It is found that, the quantum fluctuations of charge and its conjugate quantity have something to do with not only the parameters of the citcuit cells, but also the temperature.