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A theoretical method of mathematical simulation of the long-range aircraft compartments and systems thermal state are developed. To solve the direct problem, i.e. for stiff nonlinear differential equations solving, the implicit Rosenbrock method of second-order for non-autonomous systems is used. In solving the direct problem of the compartments thermal state for honeycomb core constructions the developed algorithm using a parabolic boundary value problem with discontinuous coefficients based on the numerical solution of stochastic differential equations is applied. In solving inverse problems for multidimensional heat conduction equations the developed technique with the use of derivatives assessments on the functional parameters of the expected diffusion processes is applied. As the algorithms of parametric identification of the aircraft compartments and systems thermal state model in the form of ordinary differential equations the quasi-Newton method of Broyden-Fletcher-Goldfarb-Shenno combined with the Newton's method is proposed.