I'm pretty sure the 'cooling thing' is a red herring since I understand the NG wing pumps are in the centre tank too, so that would make committing any form of aviation in an NG with an empty Ctre tank somewhat difficult
I would have expected EITHER the AFM un-modded pump restrictions (2300kg) OR NO restriction for modded pumps. I remain convinced that (if it is not an editing error) it is to prevent 'nuisance' alerts.