AbstractIn order to speed up the boiler start-up, especially from the cold state, the boiler evaporator may be flooded with hot water at the beginning of the process. The temperature of water supplied to the boiler evaporator through lower chambers of the boiler furnace chamber waterwalls will be found from the condition of equality between allowable stresses and circumferential thermal stresses on the edge of the opening for the downcomer. Two mathematical models of the evaporator hot-water heating are presented in this paper – one with lumped and the other with distributed parameters. In both cases, the water level is identical. The hot water needed to fill the boiler evaporator may be supplied from the feed water tank of another operating boiler or from a hot water vessel.