We study transport properties and the charge quantization phenomenon in a small metallic island connected to the leads through two quantum point contacts (QPCs). The linear conductance is calculated perturbatively with respect to weak tunneling and weak backscattering at QPCs as a function of the temperature T and gate voltage. The conductance shows Coulomb blockade (CB) oscillations as a function of the gate voltage that decay with the temperature as a result of thermally activated fluctuations of the charge in the island. The regimes of quantum, T \ll E_C, and thermal, T \gg E_C, fluctuations are considered, where EC is the charging energy of an isolated island. Our predictions for CB oscillations in the quantum regime coincide with previous findings in [A. Furusaki and K. A. Matveev, Phys. Rev. B {\bf 52}, 16676 (1995)]. In the thermal regime the visibility of Coulomb blockade oscillations decays with the temperature as \sqrt{T/E_C}\exp(-\pi^2T/E_C), where the exponential dependence originates from the thermal averaging over the instant charge fluctuations, while the prefactor has a quantum origin. This dependence does not depend on the strength of couplings to the leads. The differential capacitance, calculated in the case of a single tunnel junction, shows the same exponential decay, however the prefactor is linear in the temperature. This difference can be attributed to the non-locality of the quantum effects. Our results agree with the recent experiment [S. Jezouin {\em et al}., Nature {\bf 536}, 58 (2016)] in the whole range of the parameter T/EC.
