Details of turbomachines come in direct contact with gases, which are at the peak of their temperature. There is a heterogeneous temperature distribution across the detail as a result of changes in temperature and external influences. As is known, the temperature stresses in materials are due to temperature gradients and boundary conditions. However, when designing and determining the bearing capacity of turbomachinery structural elements, other factors, including the heating regime, must be taken into account. The greatest temperature stresses develop during the cycles of heating and cooling. At the same time, the greatest values of temperature gradients and stresses arise in a fairly short period of time, which in turn can cause a temperature fatigue of the material. In addition, high temperatures contribute to the development of creep deformations, which reduce the length of the life cycle of the detail. One of the factors that determines the occurrence of thermal stresses is the nature of the temperature change during the start-up process, which is determined by the start-up curve of the turbine or machine. Start-up curve is the dependence between rotor speed or gas temperature and time. It is especially important for such parts as turbine blades and roots of the blades. Considering that turbomachinery parts must withstand a significant number of start-up cycles, both temperature and mechanical analysis is required. The purpose of this work is to study the effect of the nature of the change of external temperature (start-up curves) on the change in the parameters of the stress-strain state of the fir-tree root of the gas turbine blade under thermoelastoplastic deformation, taking into account the nonhomogenous temperature distribution. The effect of heating regimes on the development of temperature stresses is considered in the paper. The initial relations of the problem of transient thermal conductivity and the problem of thermoelastoplasticity are given. An analysis of the effect of the selection of the start-up curve on the approximated geometry of fir-tree root of the blade was carried out.