Are you sure you are getting heat stress fractures and not also incomplete or asymetric weld penetration? Sulfur has the effect of increasing the weld penetration substantially. Therefore when you are welding two pieces with very different sulfur levels, you can get asymetric penetration, i.e. the weld will be at the joint on the external surface, but be away from the joint at the root of the weld. This can be overcome by careful weld set-up.
This is why most tubing has .005 to .017 sulfur, to increase penetration. I have had people tell me that 95 percent of their welders CANNOT weld tubing with lower sulfur levels. We did it every day, but it takes some experience! Valex makes tubing with lower sulfur levels.
The other comments about using a filler wire with ferrite or laser welding will definitely help reduce or eliminate weld cracking, or microfissuring.