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Fe40Mn20Cr20Ni20 medium-entropy alloy (MEA) has a single-phase crystal structure with high strength and good ductility at room temperature. It is important to study the hot deformation behavior for this alloy at a partially recrystallized state for possible high-temperature applications. In this investigation, the tensile tests were conducted on sheet materials treated via cold rolling combined with annealing at strain rates of 1 × 10−3–1 × 10−1 s−1 and deformation temperatures of 573–873 K. And the hyperbolic sine model was used to study the relationship between the peak stress, deformation energy storage and Zener–Hollomon parameter (Z parameter) of Fe40Mn20Cr20Ni20 medium-entropy alloys under high-temperature tension. According to the Arrhenius-type model, the constitutive equation of the alloys based on the flow stress was constructed, and the deformation activation energy and material parameters under different strain conditions were obtained. Based on the power dissipation theory and the instability criterion of the dynamic material model, the power dissipation diagram and the instability diagram were constructed, and the hot working map with a strain of 0.1 was obtained. The results show that the hyperbolic sine relation between the peak stress and Zener–Hollomon parameters can be well satisfied, and the deformation activation energy Q is 242.51 KJ/mol. Finally, the excellent thermo-mechanical processing range is calculated based on the hot working map. The flow instability region is 620–700 K and the strain rate is 2 × 10−3–4 × 10−3 s−1, as well as in the range of 787–873 K and 2 × 10−3–2.73 × 10−2 s−1. The optimum thermo-mechanical window is 850–873 K, ε ˙ = 1 × 10−3–2 × 10−3 s−1. [ABSTRACT FROM AUTHOR]