Quick Answer
Yes — warm water increases the release of chlorine compounds into the air, which is why the chlorine smell is stronger in a hot shower than at the cold tap. It is the same chlorine already in your supply, becoming more volatile with heat.
Problem
People notice a strong chlorine smell in the shower and wonder whether it is different (or worse) water, or something new entering the system.
Product Recommendation
For chlorine-focused shower water, ZOOSHEN KDF/carbon systems are designed for hot-water performance. See /technical/kdf-55 and /technical/chlorine.