No, the heat input doesn’t have any significant impact on the tensile strength of non-heat-treatable aluminum alloys. Instead, you have made a very common and very basic mistake—you are using the wrong filler metal. For many years people have looked at 5356 as the “universal” filler alloy for 5XXX alloys. And for the most part this is true. In the 1980s welders did use 5356 for welding 5083. However, some years ago most codes changed to require that welds in 5083 have a minimum tensile strength of 40 KSI. People soon realized that obtaining 40-KSI tensile when using 5356 is very difficult. Sometimes the tensile strength barely reaches 40 KSI. More often the tensile results are in the range of 37 to 39 KSI, as you have seen. There just isn’t enough alloy content in 5356 to guarantee that you will meet 40-KSI minimum. The 5183 and 5556 filler alloys were developed to meet this need. Both contain more alloying elements than 5356 and should always reach 40 KSI. Of the two, 5183 is more commonly used. In fact, if you look at AWS D1.2 (Structural Welding Code—Aluminum), Table 4.2, you will see that 5153 and 5556 are the recommended filler metals for welding 5083, not 5356. I believe that if you change to 5183 filler you will find that your procedure qualification difficulties will go away.