I was looking to see if I could find clips of Conan that we more candid, but he really seems the same everywhere. I think he is naturally funny and charismatic, typical of extroverts.
This is about as "serious" as I saw so far.
Skip to 2 minutes into the second video to get to the "serious" part. The life story seems like an NTP arc. The young NT obsession about what "smart people were supposed to do" and the P finding that he "loved the process" of something. It's not an awful lot to go on, however.
Ooh, I just found this, watching it now:
EDIT after watching:
His lack of separation between his work personality and himself, the constant concern for competence, the happy-go-lucky but hardworking style to his career, the way he works with his writing staff, and the fact that he is unabashed willingness to just try stuff all seems to point to ENTP.