I originally presumed that Characters that gain Willpower 'until your next turn' via temporary Great Size or other effect, such as Krangs
MOLECULAR AMPLIFICATION CHIP can't use it on their next turn.

But the ruling of Willpower on Giganta made me wonder, at what point does a character lose their 'until your next turn' abilities?

I can't find any reference to anything Before your Turn, so it must end at the Beginning of you Turn. The simultaneous ruling on Giganta would therefore imply a character like Krang using Great Size would still be able to use his Willpower.

Yes, I believe I am totally wrong, and he can't. But can someone explain in the Order of events why please?

"Until your next turn" effect expire before that turn begins. It's not currently spelled out in the Comp, but has been explained in the past.

Cheers. That is what I thought, but couldn't find anything definitive. And I've played too long to presume anything.