When you use to the advanced search, it gives you a choice to select which forum you wish to search in and by what username and a few other options in regards to when and whether you are looking for posts or threads.
For example here I have searched for any post or thread made by you in the last 30 days in descending order in the forum What's On Your Mind
Edit - You can get to advanced search by going to regular search and clicking the "more options" button.
Also, you can't actually search within a specific thread however, if you have a rough idea of when it was that you posted, then you can narrow it down by date.