The paper briefly reviews the reasons for the optical clock resonance shift due to thermal radiation. The ways to decrease thermal radiation influence with modification of the spectroscope by introducing of the cryogenic elements as an environment of the atoms from a cryogenic nozzle to create special internal chamber with the example of 87Sr optical clocks are shown. The possibility and usefulness of using the double-circuit dual-mode cryogenic chamber to suppress thermal shift in a strontium optical clocks are considered. The selection of the each element material of the chamber is based on simulated thermal distributions and heat flows of these elements. The detailed concept of this double-circuit dual-mode chamber and calculation of the shifts from each element of this chamber are also presented.