I can hear whispering at the back.*
Don't worry, I didn't misinterpret your post, I just get a bit tongue-tied.
I'm beginning to wish that I'd never raised the issue. The whole 'warmer light from cooler sources' thing can cause confusion. I think that 'warm' is used to describe light of a low correlated colour temperature more often than 'hot' is used. If director who wasn't technically-minded (and there's nothing wrong with that) asked me for 'warmer light' I'd use light of a lower CCT. If he or she asked me for 'hotter light' I'd assume that referred to the brightness, in particular more highlights. It's all about context, I guess.
*It's a publicity photo for Institute Benjamenta, or This Dream People Call Human Life by the Brothers Quay. Alice Krige as Lisa Benjamenta.