A new set-up is reported of an indirect cryogenic cooling system for a double-crystal monochromator which runs on the BM30b/FAME beamline at the ESRF (Grenoble, France). This device has been conceived to limit the vibrations on the first diffracting crystal and to maintain it at a constant temperature. These points are crucial for maximizing the beamline stability. Moreover, the relative angular position of the second crystal can be dynamically adjusted by a piezoelectric transducer coupled with a feedback system in order to always be at the maximum of the rocking curve during an X-ray absorption spectroscopy scan. The temperature is stabilized to an accuracy of 0.01 degrees , with two principal consequences. The energy resolution is close to the theoretical value [DeltaE/E = 5.6 x 10(-6) for Si(220)] and the precision of the energy positioning is extremely good even if the power load changes. A feedback mechanism allows a permanent and automatic optimization of the angle between the two crystals of the monochromator. The intensity of the monochromatic beam remains optimized (i) when the intensity of the electron beam decreases in the storage ring and (ii) during an energy scan.