The Ni–Mn–Ga ferromagnetic shape memory alloys (FSMAs) are a group of active materials that undergo martensitic transformations (MTs) induced by temperature, stress and/or magnetic fields, resulting in large recoverable mechanical deformations. Their fast response and high energy density make them ideal candidates for implementation in sensors and actuators. Recently, the development of high-temperature FSMAs (HTFSMAs), working at temperatures over 373 K, has become an important task to meet the current requirements of modern technologies. The magnetic and magnetoelastic properties of FSMAs are very sensitive to the interactions between the magnetic moments of atoms that, in turn, depend on the atomic positions within the lattice. Here we investigate a series of the polycrystalline Ni45Mn25-xGa20Co5Cu5Fex (x = 0, 1, 2 and 5 at%) HTFSMAs. Their MT and Curie temperatures, the crystal structures of the martensitic and austenitic phases, the temperature evolutions of the lattice parameters of both phases and the atomic site occupancies have been studied by means of powder neutron diffraction measurements, complemented by standard characterization techniques. Based on the atomic site occupancies and additional measurements of the saturation magnetization, the influence of the structure and atomic ordering on the magnetism in these materials is analysed. The most promising candidate for high temperature magnetic actuation is the alloy with Fe 5 at%, following a combination of the high MT and Curie temperatures, around 370 K and 440 K, respectively, with a low tetragonality ratio, c/a ≈ 1.16, in the proximity of MT.