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Martensitic transformation in Ni(2+x)Mn(1-x)Ga alloys is known to be controlled by the soft tetragonal elastic constant C' of the high-temperature austenitic phase. The temperature (T) and composition (x) dependence of C'(T, x) are calculated using the first-principles exact muffin-tin orbitals method. We show that the temperature factor of C' is dominated by the phonon-smearing term. The competition between the negative alloying effect (partial derivative C'/partial derivative x < 0) and the positive temperature effect (partial derivative C'/partial derivative T > 0) is found to lead to nearly constant C'(T(M)(x), x) at the critical temperature TM(x). We demonstrate that a proper account of the temperature and composition dependence of C'(T, x) is indispensable for reasonable theoretical TM(x) values. VC 2011 American Institute of Physics. [doi: 10.1063/1.3603935]

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