A MEMS resonator system has a micromechanical resonant structure and an electronic processing circuit including a first resonant loop that excites a first vibrational mode of the structure and generates a first signal at a first resonance frequency. A compensation module compensates, as a function of a measurement of temperature variation, a first variation of the first resonance frequency caused by the temperature variation to generate a clock signal at a desired frequency that is stable relative to temperature. The electronic processing circuit further includes a second resonant loop, which excites a second vibrational mode of the structure and generates a second signal at a second resonance frequency. A temperature-sensing module receives the first and second signals and generates the measurement of temperature variation as a function of the first variation of the first resonance frequency and a second variation of the second resonance frequency caused by the temperature variation.