This is something I admit I am very guilty of. Someone emoting a thought and I respond to it and then have to think of some reason I all of a sudden have the power of mind reading. Usually, I mumble something about reading their facial expression and making an educated guess and then walk away embarrassed. This post is to prevent you from making my mistakes.
Typically thoughts are displayed through an emote. I've played games in the past that made the distinction between a thought emote and an action emote with a special speech bubble for thoughts. WoW does not have that so you just have to read a little more carefully than I and you will be successful.
Having the thoughts splashed across your chat window creates the temptation to react or comment about them. Technically these thoughts were just dialog in the person's head and a conversation you should not be privy to.
So why would thoughts be used in role-play? Well the best examples I've witnessed was to help the thinker sort of describe where they are going with the discussion. The information they are providing is not to be reacted to but provides some information on the discussion that otherwise you would have no idea.
Desdarii: I really dislike rogues.
Desdarii sits in quite contemplation of the specific battles where certain horde rogues have plagued her existence.
This isn't a great example. Like I said, I typically do not role-play in this fashion so just pretend it's very relevant and helpful example for my sake. If you only heard Desdarii's statement you would assume she meant all rogues even her allies. The thought clarified her position by showing she was particularly thinking of enemy rogues in certain battles. Although it would not be correct in commenting back about how you also dislike Horde rogues, you would not have to immediately take offense and challenge her to protect the honor of all rogues everywhere. You could ask Desdarii what she means by her comment to further the conversation and keep things civil. Perhaps Desdarii is trying to steer the conversation into a discussion about one of those particular battles she is thinking about.
Whether or not you chose to type out your characters thoughts is up to you. I mainly wanted to make it know that there are role-players out there who do this and try to protect you from the role-play blunders I find myself in.