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The single-pass thermal compression experiments were conducted on NiCoFeCrAl high entropy alloy by Gleeble-3800 thermal simulation tester. The Arrhenius constitutive model was established based on the peak stresses. With four instability criteria (Prasad, Murty, Gegel, and Malas), different heat processing maps of dynamic material model were established. The applicable ranges of the instability criteria for the alloys in the heat deformation process were analyzed and compared. Results show that the optimal heat processing ranges of the alloys are the temperature range of 980–1010 °C+strain rate of 0.01–0.001 s^-1 and the temperature range of 1050–1100 °C+strain rate of 0.01–0.1 s^-1. The average power dissipation rate is greater than 36%. Through EBSD microstructure analysis, the softening mechanism of thermal deformation is changed from dynamic recovery to dynamic recrystallization with increasing the deformation amount.