I am in the middle of itwith NewT. I have experienced this before with PrevGoodT.
Mine feels like "intense love," as you put it. I also describe it as a severe "homesickness" feeling for T.

These two therapists seemed to roll with it, act like it is beneficial to my therapy. "You feel how you feel," they tell me.

Any good T is already prepared to listen to these feelings from you. They seem to know what I need before I realize it.
I have read that transference is a need being fulfilled.