Hmm... I'm using the ESky 11.1v 1000mAh packs too, but mine seem to get hot. Not hot enough that I can't hold it after a flying session, but hotter than I'd like.
I use 7.4v 800mAh packs on my CX2 and Honey Bee FP. After flying those helis, their respective batteries are warm, not hot.

I'm thinking that the ESky packs might not be the best choice for the Axe CP.