How do deaf people think if they can't 'hear' words in their heads? What language do they use and how does it work?The answer is quite interesting. Here are two attempts to describe the answer. First here is the Cecil Adam's take from The Straight Dope. The second one is How Deaf People Think from Today I Found Out.
It just goes to show that the human mind is incredibly resilient and powerful. Remove the ability to hear and it still finds a way to think and acquire language.