The mesoscopic capacitor coupled circuit of 3 meshes can be considered as the canon- ical ensemble. It gets at quantum fluctuations of both charge and magnetic flux in the coupled circuit at a finite temperature by calculating the density matrix of the canonical ensemble. Our results show that quantum fluctuations of both charge and magnetic flux depend on the tem- perature. With high frequency, charge fluctuation, which are similar to the situation of low temperature, show typical quantum noise, and it is impertinent to temperature. But magnetic flux fluctuation not only is quantum fluctuation of zero point temperature, also is always con- nected with temperature. At absolute zero point temperature, the uncertainty relation of both charge and magnetic flux in the input mesh or in the output mesh is constant.