The rear wall of the header box serves as a tubesheet in heat exchangers of double plate header box. Tube-to-tubesheet welding must be performed using orbital Gas Tungsten Arc Welding (GTAW) with a head extension, which is passed through the corresponding hole in the front wall (plugsheet) of the header box, where the welding machine is supported. In this project, the effect of parallelism deviations between the plugsheet and the tubesheet of carbon steel header box is analyzed to evaluate its influence on the quality of the tube-to-tubesheet welding. Welded tube (SA-210 Gr. A1) to tubesheet (SA-516 Gr. 70) coupons are manufactured simulating the parallelism deviations previously analyzed in two double plate header boxes of air-cooled heat exchangers using two different preheating temperatures. Macrographic analysis is performed in order to evaluate the weld penetration (minimum leak path) and length of the weld leg in tube-to-tubesheet joints. The results obtained show important variations in those parameters when the parallelism deviations are equal to or greater than −1 mm over the theoretical distance as well as when the distance approaches +1 mm or more. Finally, the incorporation of dimensional controls prior to the welding process is discussed and the implementation of improvements in orbital GTAW equipment is recommended as an optimal solution for this kind of heat exchangers.