This is a good example of the uncertainty of heat input.
The equation used by most of us involved with welding is Q=(IxEx60/V) where I is amperage, E is voltage, and V is the travel speed. What isn't accounted for is the efficiency of the welding process, i.e., how much of the energy is actual transferred into the weld puddle.
The welding process and the welding parameters influence the energy per unit time introduced into the weld. That being the case, you can select a welding process such as GTAW that has inefficient heat transfer and low welding amperage, a short arc length and high travel speeds to minimize the energy introduced into your part. A cool down period can be used to allow the heat to dissipate before doing damage to you part.
Since the material being welded is unlikely to form martensite upon cooling, you can hasten the cooling between passes with a blower or with wet rags applied to the area adjacent to the socket joint.
Best regards - Al