Abstract: A process for thermally stress-relieving a stressed portion of a metallic tube is disclosed herein. The process generally comprises the steps of inserting a small diameter radiant heater into the open end of the metallic conduit and then positioning it adjacent to the portion to be stress relieved, and heating this portion to a temperature between about 1150.degree. F. to 1500.degree. F. for a time period of between about four and twelve minutes, depending upon wall thickness. In order to determine the proper amount of electrical power to apply to the radiant heater, the emissivity of the stressed portion of the conduit is first measured by heating a portion of the section to incandescence at a known power level, and then determining the temperature of the incandescent tube by means of a pyrometer which compares the intensity of two selected colors or wavelengths of the transmitted light. This process is particularly useful in thermally stress-relieving the U-bends of heat exchanger tubes formed from Inconel.