We present a systematic experimental and theoretical study of the first-order phase transition of epitaxially grown MnAs thin films under biaxial tensile stress. Our results give direct information on the dependence of the phase-transition temperature of MnAs films on the lattice parameters. We demonstrate that an increase of the lattice constant in the hexagonal plane raises the phase-transition temperature (T-p), while an increase of the perpendicular lattice constant lowers T-p. The results of calculations based on density functional theory are in good agreement with the experimental ones. Our findings open exciting prospects for magneto-mechanical devices, where the critical temperature for ferromagnetism can be engineered by external stress.