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For the first time, the high Q components of the optoelectronic oscillator, i.e. the optical fiber, and the narrow pass band microwave filter in the oscillator loop were thermally stabilized to improve the oscillator short- and long-term frequency stability. In our design, the temperature of these elements is kept above ambient and stabilized with the help of resistive heaters and temperature controllers. With this scheme the free running oscillator demonstrates a short-term frequency stability of 0.02 ppm and frequency vs. temperature slope of -0.1 ppm/°C (at 20-30°C) with an exceptional spectral purity (-143 dBc/Hz at 10 kHz offset frequency). Locking the opto-electronic oscillator to a standard reference oscillator, oscillating at 100 MHz further stabilized the 10 GHz microwave carrier frequency.