The effect of stress state on the thermally activated processes of $L1_{0}$-FePt-ordered phase formation at annealing as well as the magnetic properties of Fe$_{52}$Pt$_{48}$(15 nm) film are studied by the physical materials science methods. The film is fabricated by magnetron sputtering technique on monocrystalline Al$_{2}$O$_{3}$ ($10\bar{1}0$) sapphire substrate. Rapid thermal annealing in nitrogen atmosphere carried out with heat rate of 400°C/s in temperature range of 500–800°C for 30 s. As determined, the disordered $A1$-FePt phase is formed in as-deposited film, and tensile residual mechanical stresses are presented. At the heating up to 500°C, the sign of stresses is changed, and the last ones become compressive. The $A1$-FePt $\rightarrow$ $L1_{0}$-FePt phase transformation starting at annealing temperature of 600°C is accompanied with both the lattice cell volume decreasing and the stress relaxation, and induces the change of magnetic properties. Further annealing temperature growth up to 800°C leads to increasing of both the amount of hard magnetic $L1_{0}$-FePt-ordered phase and the coercivity in applied magnetic field up to 14 kOe, which is perpendicular to film surface. Meanwhile, isotropy of magnetocrystalline energy is maintained.