From your description of his actions and words at face value, I don't think there's enough to conclude that he is attracted to you, although you are actively interpreting that to be the case (labeling him "lovesick," "dreamful," and "adoring," describing his actions as "lovingly"). It's likely that, as you put it, it is "just his personality" and he is simply a warm and charismatic person and your good interpersonal chemistry is just starting to pick up, and he feels affection for you.

It's also possible that talking about sex with him awakened some new thoughts and feelings in you. I find that talking about sex with someone—like a friend—almost invariably for me, deep down, brings my attention to that person as a sexual creature. The content of the conversation as well as the openness it requires can plant seeds of infatuation. Maybe those feelings lead to wishful thinking, hence your interpretative adjectives like "adoring" and "lovesick" (and let me tell you, I know what wishful thinking is like! I am a master-pro).

Or, he could actually be attracted to you. I just don't think there's enough definitive information to conclude that, on my part, with the limited info. Some demeanors and nuances can be so subtle in therapy that you really need to be there to witness and understand it.

I'm sorry this isn't more help and that I don't think anyone can really give you yes-or-no answer quite yet, but I can say that it's important to explore those feelings and ask yourself where they are coming from. When someone listens to all your problems and shows concern and intelligent feedback, it's a task not to like them. If you're feeling exceptionally brave you could even bring it up to him and he could help you sort it out. I still have to work up the nerve to tell my own therapist my overwhelming transference feelings. You can keep us updated, either way!