Steel is one of the most widely used construction materials. The key to its success is the large variety of material's properties which can be obtained by simply changing the processing parameters. In the presented study we focus on the effect of thermal processing parameters on the formation of martensite and bainite. Since carbon diffusion is a temperature activated process we investigate its effect on the formation of bainite vs martensite depending on the cooling rate and holding temperature considering also the release of latent heat. To fully account for the large transformation strains during the martensite and bainite formation a finite strain mechanics formulation is used in our simulations. Plastic relaxation as well transformation induced lattice rotations resulting in 24 Kurdjumov-Sachs martensite variants are also considered. Thus, the evolution of temperature, composition, stresses and strains as well as the microstructure are simulated simultaneously within the phase-field framework. The analysis of simulated martensite and bainite microstructures, including the distribution of composition, residual stresses and resulting strains will be presented. The effect of thermal processing parameters influencing carbon diffusion and partitioning during the transformation will be discussed in order to explain the difference in the formation of bainite and martensite.