Temperature dependences of low-field quasistatic magnetic susceptibility in the vicinity of martensitic transitions in an NiFeGa alloy are studied both by experiment and analytically. Pronounced reversible jumps of the magnetic susceptibility were observed near the martensitic transition temperature. A general description of the temperature dependences of the susceptibility in ferromagnetic austenite and martensite phases and the susceptibility jump at the transition is suggested. As a result, the main factors governing the temperature dependences of the magnetic susceptibility in the magnetic shape memory alloys are revealed. The magnetic susceptibility jump value is found to be related to changes of: (i) magnetic anisotropy; (ii) magnetic domain wall geometrical constraints (those determined by the alignment and size of twin variants) and (iii) mean magnetic domain spacing.