Ok, but what is RESTful thinking?

The way i think about REST is this: here is my stateful application, how can i make it available over HTTP/REST. So i start identifying resources. Most of them are easy - they map to your domains models. But some of the operations on some of the resources are quite important to my application (eg: ordering products, making a payment etc), so i consider creating separate resources for them.

It looks like you are referring to modeling your stateful application when you talk about RESTful thinking.