Case Hardening Distortion Compensation
Process-technical and geometric measures during heat treatment to minimize and intentionally control unavoidable dimensional changes.
Case hardening and distortion compensation are two different things. When welding, you always get stresses and distortion in the part due to heat input. If you want to case harden a part, you usually do it before welding or you grind the hardened zone again after welding. The idea of compensating hardness differences via special cooling after welding doesn't work that way. If you want to control hardness and distortion after welding, look at the heat input, keep the interpass temperature, and if in doubt, do a stress-relief anneal. The exact temperatures and times depend on the material, you have to check the data sheet.