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The transition from a one-dimensional analysis of the thermal process in the flat sample to the analysis of rather complex thermal process in a cylindrical sample, as close as possible to the actual product. This resulted in the development of the mathematical apparatus for solving multidimensional problems of heat conduction and creation of hardware and software thermal control.

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The paper considers the circuit engineering and structural-technological basis of new devel-opments of special-purpose microcircuits, the prospects for its development are determined. The complexity of solving the problem is established, which consists in a complex combination and elimination of contradictions of various principles of creating equipment. It is assumed that the particle enters the circuit at a time equal to the beginning of switching. The frequency of the chip is 30 MHz, which corresponds to most of the frequencies that are used in spacecraft.

The article studies the mathematical apparatus, being the basis of information support of the methods of non-destructive thermal control of heat-shielding properties of samples from solid heterogeneous or monolithic materials using rectangular heated surface area. When developing the mathematical apparatus we used Laplace and Fourier transformations which let the developed method of integral characteristics greatly simplify the search for solutions of multi-dimensional problems of thermal conductivity and get explicit and accurate analytical expressions to determine thermal conditions.