The article deals with the problem of the influence of the dynamic crystallization conditions on the structure and on the martensitic transformation in amorphous Ti_40.7Hf_9.5Ni _39.8Cu₁₀ thin ribbons. The crystallization was realized in a DSC apparatus by heating the samples at different heating rates. DSC and X-ray diffraction were employed to study the martensitic transformation and the structure of the crystallized ribbons. The data show that increasing heat rate resulted in an increase in the crystallization temperature, a decrease in the B2 ↔ B19' transformation temperature and an extension of the halfwidth of (110) reflections of the B2 phase. It is concluded that the increase in the heating rate decreases the grain size of the crystalline phase. As the temperature of the B2 → B19' transition depends sensitively on the grain size the heating rate could be used for controlling the characteristics of the phase transformations.