Since the start of this year I have been thinking to myself in Japanese several times throughout each day. I am not sure if it's ever appropriate to use んだ in such self-directed speech. One scenario where I consider using this is when I suddenly realize something, e.g.
じゃ、家に帰ろう。あ、まずメールを送るんだ。
Does this make any sense? If not, when would you use んだ in your thoughts (if at all)? I understand that this construction is used for conveying new information, but philosophically speaking you already have all the information when you're thinking to yourself.