In the framework of the study, the temperature dependence of the elastocaloric effect in [001]-oriented Ni50Mn30Ga20 single crystals was investigated. The elastocaloric cooling with a high adiabatic temperature change ΔTad > 5 K was observed in a wide temperature range of superelasticity of 373–453 K. It was found that a change in kinetics of stress-induced martensitic transformation (diffusing of transformation) with increasing of test temperature and deforming stresses leads to a decrease in the adiabatic temperature change ΔTad from 6.8 to 5.0 K.