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A Fabry-Perot resonator operating at 39 GHz, with two pairs of quarter-wavelength single-crystal quartz Bragg reflectors has been realized. For the length of 98.26 mm, its Q-factor is about 560,000, which is 4.3 times better than for the same resonator without Bragg reflectors. Rigorous finite-difference frequency-domain analysis has been applied to the problem and is compared with simplified semi-analytical solutions. Good agreement between theoretical and experimental resonant frequency and Q-factors has been obtained. Thermal compensation of the resonant frequency of the Fabry-Perot has been proposed employing rods and cylinders made of metals with different thermal expansion coefficients.