An artificial channel-cut crystal monochromator for the hard X-Ray beamlines of SASE 1&2, cryogenically cooled by the so-called pulse tube cooler (cryorefrigerator), is currently under development at the European XFEL (http://www.xfel.eu/). The fabrication is on-going. We present here the crystal optical consideration and the novel cooling configuration, according to the X-Ray FEL pulses proprieties. The mechanical design improvements are pointed out as well to implement such kind of monochromator based on the previous similar design.