A field and/or temperature hysteresis is more than just an interesting incomprehensibility that occurs in materials with a first-order magnetic transition. Indeed, the reversibility of the magnetocaloric effect (MCE), being essential for magnetic heat pumps, strongly depends on the width of the thermal hysteresis and, therefore, it is necessary to find solutions to minimize losses associated with thermal hysteresis in order to maximize the efficiency of magnetic cooling devices. In this work, the polymer matrix composites with MnAs powder as reinforcing material were obtained and its MCE by direct method was studied. The influence of composite preparation process on the MCE was investigated. It was found that the MCE of bulk MnAs shows strong temperature hysteresis caused by magnetostructural transition from paramagnetic to ferromagnetic state, which also leads to an irreversible MCE at cooling at first magnetization. The reversible MCE of bulk MnAs in field 12.5 kOe is ΔT ∼ 0.4 K. It was shown that Mn-based polymeric composite cured in aligned magnetic field presents a reinforcement of the MCE temperature hysteresis. Thus, the MCE value in aligned composite is less than the value of the MCE in the bulk MnAs. It was shown that the decreasing of linear size of MnAs grains in the polymeric composite leads to sharp decreasing of the MCE to value of 0.05 K. It was established that the optimal properties, such as giant MCE and low temperature hysteresis, are found for composite hardened under pressure of 10 kBar. In this composite an increase of reversible MCE (compared to the bulk MnAs) till to the value of ΔT ∼ 1.2K was observed.