So instead of the canned reply that does nothing but scream "I'm an asshole," I'll actually use these to answer OP's question.
Deaf guy here. I just think visually, like with imagery and pictures. Only time when I think in sign languages is when I'm talking to another deaf people.
-comment with an AMA from /u/BrushGod who has always been deaf.
As I have mentioned before in other threads, it's all visual for me. I am not born Deaf but actually lost my hearing when I was one year old to spinal meningitis. Many of my thoughts and dreams are when I am imagining seeing myself in a 3rd person perspective doing various of things. Being a bank robber, giving an inspirational speech in front of thousand of people, or even doing my pickup art on some hot chicks. Even when I am sitting alone, mentally preparing for a big meeting where I will lead, I will be visually imagining myself standing in front of a powerpoint with all the colorful graphs and seeing the other people's faces watching me. I would think of all the lines that I am to say. Also what kind of questions I would face. It's all visual because my interpreter is involved with sign language. I have no idea what sounds sound like ...nor would I know what it sounds like for any words to be spoken to me. I have no way of imagining what a spoken word or even any type of noise. Such as knocking at the door. When I think of it happening, I visually imagine people turning their heads toward the door and then the door opens. That's how I think of what a knock sounds like.
-comment from /u/silencegold.
My two younger brothers are completely deaf. Both of them got cochlear implants around the age of 2-4. They hear fine now and speak normally but both say that they dream without sound, just pictures. Both of them often go hours at a time without hearing (they must remove the earpiece to swim in a pool or something) and they can't ever seem to explain what it feels like to have a complete lack of sound. They say they have a hard time imagining sounds inside their brains. I guess they think mostly in pictures.
-The most relevant comment I could find from /u/bobthedude56