I'm wondering what it is like to publish a PhD thesis commercially? Has anyone done that before? What would the contract be with the publisher regarding sales profits?
The answer to this question is very field- and country-dependent. In the sciences, a thesis is very rarely transformed into a book (except in certain locations, such as Germany), while in the humanities it is a relatively common end for high-quality theses. To a first approximation, this is because science theses are often best "republished" or "prepublished" as a set of several peer-reviewed journal papers, whereas it is more common for a humanities work to be a single large monograph not suitable for such sub-publication.
There are a large number of pseudo-scam organizations which will contact you and offer to turn your thesis into a book. Don't bother with them: they will merely waste your time and taint your reputation.
Instead, I would recommend beginning with a discussion with your advisor, who will know the common practices in your field, and may be able to help assess whether it is a good idea to publish your thesis as a book at all. You may also contact a reputable university press, who can help assess your work and guide you through the process of transforming it.
No matter what, however, don't expect to make any significant amount of money from such a venture.