If I concentrate, I can sense something akin to the typical "internal monologue", but it isn't present enough to be copied down, and even when it is it tends to move so fast that I only really get the conclusion.
When I started coding, as a teenager, I'd pace around the room explaining things to myself almost as if I was giving a lecture, so it's fairly baked into my thinking process. If you assert something, laying a statement out there, the process of hearing it can cause you to start to think other things: is it actually well-justified, are the assumptions behind it solid; what are the consequences and implications of the statement; all the things you might think if you heard someone else say something, and you're listening critically and intently.
If you use a text editor you don't need to write everything down right away. You can just dump a keyword or a snippet that describes or is associated with what you're doing, note your intent and/or your goal, and as you work on your task keep updating your notes whenever you get the time.