Wind farms and other renewable energy sources are characterised by the high unpredictability of generated power as a function of time. When the wind velocity decreases, the power generation diminishes rapidly. To offset the loss of power in the energy system, thermal power plants should be designed for quick start-ups and shutdowns, i.e., the flexibility of thermal power units should be improved. The pressure and temperature of the working fluid in the boiler should be increased quickly, so as to shorten the start-up of the boiler. The subject of the book is inverse heat transfer problems occurring in the monitoring of thermal stress in pressurised thick-walled components. New methods of determining the optimum time variations of fluid temperature during heating and cooling of the pressure parts in thermal power plants are presented. A new technique for measuring the transient temperature of fluid flowing in the pipeline are also presented. Numerous examples that illustrate the practical application of theoretical methods developed are presented as well. The book is meant for engineers, researchers, and scientists. It can also benefit the students of technical universities. The book may be helpful to manufacturers of large power boilers and users of thermal power plants, both conventional and nuclear.