An experimental study is made into the process of heat transfer from a pulse-superheated probe to a solidified polymer system at probe temperatures above the temperature Td∞ of the beginning of thermal destruction of matter in a quasi-static process. Use is made of the procedures of thermal stabilization of the pulse-superheated probe (with the characteristic time of constancy of superheated probe temperature of 1 ms) and of shock heating (with the characteristic time of increasing the probe temperature of 1 μs and that of monitoring its cooling-down of 1 ms). The effect of short-term thermal stability of polymers in the region of T > Td∞ is revealed. A procedure is developed for identifying the signs of thermal destruction of polymers in the pulsed process. The maximal values are estimated of the density of heat flux through samples without their thermal destruction.