Although she keeps saying attachment in therapy is inevitable, and although she 'feeds' the attachment by staying in email contact, I also experience her as cold - obviously not as uncaring, I think she proves with every email that she cares, but she is incredibly distant.
I think you could experience any therapist as anything - attachment issues are going to come up with anyone, whatever they do.
If she didn't have boundaries, that would be unprofessional and potentially disastrous for managing the attachment. Yet if she does have boundaries, she can be perceived as withholding.
If your therapist has been deliberately and calculatedly following a hot and cold strategy in order to provoke your attachment issues then that's a different thing. I'm still unclear on that.