Hurlburt has great research on this using Descriptive Experience Sampling.
Some people mainly use images, others mainly speech, others mainly emotion etc. And many more use a varied mix.
Also the way each modality of thought is used is hugely variable - exactly what people see and with what quality or how precisely they feel emotional in their body etc.
To me it explains a huge amount of how different people are good at different skills.
I've a podcast on this topic ("Imagine an apple") if you're interested in more.
Let me ask, when you decide what to eat for dinner, how do you arrive at the answer? I visualize what's in the fridge, what I can cook with the ingredients. Or if I want to eat out I visualize our neighborhood like Google Maps and look around at the different options.
When I'm solving an algorithmic problem I visualize the data, spatially if possible otherwise just as text, lists or vectors. It's like I'm using a notebook but it's faster and a bit more fuzzy.
Sometimes it's a keyword/concept thing where I'll think of the main items and I get a feeling that I know how to fill in the blanks. I haven't actually visualized or verbalized what would fill those blanks though (and sometimes the feeling is wrong).
I think pretty much all of the senses can be used to do some form of thinking. I can imagine songs in my head, touch, feelings etc. Rarely are they useful for problem solving though, but some of these are nice for falling asleep in unknown environments.
Oh and then there's the thinking where nothing seems to happen. I stare at a piece of paper and after a while I know what to do next. How did I arrive at that conclusion? I don't know, but it definitely wasn't verbal, visual, aural or anything else. This tends to not solve complex problems like math, but it basically tells me what I should do to try to solve it (usually verbal or visual).