A fast way of temperature and thermal stress evaluation in complex-sha
ped pressurized elements is presented. Transient temperature and therm
al stresses in the point of concentration were calculated using the di
screte form of the Duhamel integral. The time changes of temperature a
nd maximal stresses u((r) over right arrow, t) were calculated for uni
tary step change of the fluid temperature using the Finite Element Met
hod. The Duhamel integral was then approximated numerically and the te
mperature and thermal stresses were then evaluated for arbitrary time
changes of fluid temperature. Practical application of the presented m
ethod was illustrated by determining the circumferential stresses on t
he edge of the boiler drum-downcomer joint.