If you keep in mind that I am not immediately familiar with the material in question, in general minimum heat input can be as critical to impacts as maximum, especially when the toughness of the mateiral relies on tempering from subsequent weld beads. One of the ways is that lower heat input does not penetrate its energy as deeply as high high heat input and therefore a smaller volume fraction of tempered weld metal may result, which can reduce toughness. Even if you PWHT there are other factors such as carbide precipitation which can be increased through subsequent beads and improve toughness. In some cases higher heat input can temper HAZ's better. In reality toughness is not exclusively controlled by maximum heat input. Thats just the general thinkng because thats what most code bodies and/or specifications impose based predominantly on grain size emphasis.
High heat input may cause larger grain size but those grains may be tempered better than smaller grains.
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