Two methods for monitoring the thermal stresses in pressure components of thermal power plants are presented. In the first method, the transient temperature distribution in the pressure component is determined by measuring the transient wall temperature at several points located on the outer insulated surface of the component. The transient temperature distribution in the pressure component, including the temperature of the inner surface is determined from the solution of the inverse heat conduction problem (IHCP). In the first method, there is no need to know the temperature of the fluid and the heat transfer coefficient. In the second method, thermal stresses in a pressure component with a complicated shape are computed using the finite element method (FEM) based on experimentally estimated fluid temperature and known heat transfer coefficient. A new thermometer with good dynamic properties has been developed and applied in practice, providing a much more accurate measurement of the temperature of the flowing fluid in comparison with standard thermometers. The heat transfer coefficient on the inner surface of a pressure element can be determined from the empirical relationships available in the literature. A numerical-experimental method of determination of the transient heat transfer coefficient based on the solution of the 3D-inverse heat conduction problem has also been proposed. The heat transfer coefficient on the internal surface of a pressure element is determined based on an experimentally determined local transient temperature distribution on the external surface of the element or the basis of wall temperature measurement at six points located near the internal surface if fluid temperature changes are fast. Examples of determining thermal and pressure stresses in the thick-walled horizontal superheater header and the horizontal header of the steam cooler in a power boiler with the use of real measurement data are presented.