The efficiency of predicting the deformation of woven polymer composite materials at high temperatures taking into account the processes of ablation and thermal oxidative degradation is analyzed within the framework of hereditary media mechanics. Ablation is understood as burnout of a part of the composite components’ mass, while degradation is a change of its properties under the influence of heat at high temperatures. Dependences, which describe the change in the relative density of the composite, are illustrated by the thermogravimetric analysis curves obtained at a fixed heating rate. Numerous experimental studies have proved that the equation of state of ablution polymer matrices, carbon fiber bundle, and woven composites depends on the temperature and heating rate. The reliability of the calculated deformation results is evaluated by comparing them with the experimental data obtained for the quasi-static heating conditions of the epoxy woven carbon plastics specimens. The composite is reinforced with carbon plastic woven fabric of the canvas type. It is shown that the functions aθ1 and aθ2, which take into account the effect of fabric on the elastic characteristics of the composite in the main directions, quite effectively describe their distributions depending on the maximum angle of curvature ϑm of reinforcement threads, the temperature θ and the mismatch angle Φ under tension and shear in the reinforcement plane. At low temperatures before the ablation process, the Young modulus values practically return to the initial ones. After completion of the ablation process observed at θ≥ 500°C, the material is completely charred, which correlates with the experiment. A good agreement of the distribution of thermal strains at a fixed heating rate θ ≈ 0.1K/s with the experimental results can be noted.