I think that maybe what makes gratitude seem "clingy" has something to do with insecurity on the part of the person doing the thanking. I've gotten 'thanks' before from people who seemed desperate to make me understand just how much they appreciated whatever I did--It's like they wanted something back, some show of emotion from me that would validate and reflect the intensity of their thanks....Like they wanted some proof that they were as special to me as I was to them.

Which is only natural, right? You put yourself in a vulnerable position when you feel deeply about someone and risk that depth not being returned.

Maybe the best way to go about it is to assure yourself beforehand that T will accept both you and your thanks? Remind yourself that the relationship is secure and you won't be rejected for showing gratitude/emotion? A sincere, but not desperate, "I am enormously grateful for your help" ought to do the trick.