For the mesoscopic capacitance coupling LC circuit, the Hamiltonian is given by the canonical quantization. The Hamiltonian operator is diagonalized by a unitary transformation. The ensemble average energy and its fluctuations are derived by ensemble theory. In virtue of the generalized Hellmann-Feynman theorem, the quantum fluctuations of charge and self-conductance magnetic flux for the system at finite temperature are investigated. It is found that, the quantum fluctuations of charge and self-conductance magnetic flux depend on the temperature as well as the parameters of the circuit components.