Having a character think for himself really pushes the player into the "Guardian Angel" role, in that he's just there to keep the character from dying. Which, works well enough given an appropriate design.

As for a specific window. This really depends on the style of the game. For example, if you're using comicish bubbles with the little triangular arrow to point at who said what, then the bubble with detached bubble for thought is the obvious way to go.

Likewise, if you had a specialized text window that always appears on a specific part of the screen, and along side it a portrait of the character speaking; then a smaller thought window, semi-transparent, with a smaller portrait of the playable character making some thoughtful grimace, thats the way you'd want to go there.

Then theres the possibility of a silent but witty narration. I remember watching a show, I think it was on TechTV before G4 claimed it, about inventors. The show didn't have a verbal narrator, it had yellow text along the bottom left of the screen.

However, I should warn in advance to maintain your gimmicks and don't break them. A character thats always thinking would seem odd if he started talking. If he needs to talk though, you need to find the happy medium between the two.