From a Paris Review interview with Italo Calvino:
I could try to improvise but I believe an interview needs to be prepared ahead of time to sound spontaneous. Rarely does an interviewer ask questions you did not expect. I have given a lot of interviews and I have concluded that the questions always look alike. I could always give the same answers. But I believe I have to change my answers because with each interview something has changed either inside myself or in the world. An answer that was right the first time may not be right again the second.
This is pretty much exactly my experience being interviewed. You want to sound fresh and interested in the question, but you also need to negotiate against a couple possibilites: that you're likely to be answering a question you've been asked before (in a satellite radio tour, something you've been asked ten minutes before); or you're asked something you've never really thought about, and so have to actually come up with something interesting on the fly.
Thinking out loud never sounds that interesting (at least not when I do it). Audiences like it when you've thought of something, not when you're thinking of something.