One of the important stages in the creation of the scientific and technical foundations for the calculation, design and manufacturing technology of the lowest heat-conductivity thermal protection from screen-vacuum thermal insulation (SVTI) is the development of a process for achieving the optimal vacuum P0 ≤ 10−3 Pa in the SVTI layers, since at this pressure, thermal conductivity (λeff) through the SVTI is carried out only due to the radiant (λrad) and contact-conductive (λ k, k) components. It is proposed to obtain such a pressure in thermal insulation by using cushioning material in it, which was previously degassed in a separate vacuum chamber at 370−380 K for 12 h in order to remove water molecules from its structure and then replace them with nitrogen molecules. These molecules have 3−4 times less heat of adsorption; therefore they are pumped out faster. As a result, it becomes possible to accelerate (by ∼20 h) to achieve optimal vacuum in thermal insulation, as well as 11% lower effective thermal conductivity [equal to (14.1−14.3)⋅10−5 W/(m⋅K)]. The analysis carried out (according to the developed methodology) showed that the achieved optimal effective thermal conductivity of thermal insulation in a cryocontainers is determined by 33% of radiant thermal conductivity [4.7⋅10−5 W/(m⋅K)] and 67% of the contact-conductive component [9.4⋅10−5 W/(m⋅K)].