The properties of widely used Ni–Ti-based shape memory alloys (SMAs) are highly sensitive to the underlying microstructure. Hence, controlling the evolution of microstructure during high-temperature deformation becomes important. In this article, the “processing maps” approach is utilized to identify the combination of temperature and strain rate for thermomechanical processing of a Ni42Ti50Cu8 SMA. Uniaxial compression experiments were conducted in the temperature range of 800–1050 °C and at strain rate range of 10−3 and 102 s−1. Two-dimensional power dissipation efficiency and instability maps have been generated and various deformation mechanisms, which operate in different temperature and strain rate regimes, were identified with the aid of the maps and complementary microstructural analysis of the deformed specimens. Results show that the safe window for industrial processing of this alloy is in the range of 800–850 °C and at 0.1 s−1, which leads to grain refinement and strain-free grains. Regions of the instability were identified, which result in strained microstructure, which in turn can affect the performance of the SMA.