Short Answer
Well, if you take for "pure thought" the heavily a priori notions of rationalism, then, many professional philosophers believe that empiricism and a posteriori thinking play an important role in a sensible philosophical worldview. As such, they openly embrace science, and do not see a crisp line of division between philosophy and scientific fact. In fact, many famous 20th century philosophers have some relationship with what is termed a natural epistemology, and some very sophisticated philosophers have argued there is no line between the two at all.
Long Answer
It should be noted that "thought" is a word with some ambiguity in philosophy, and is a term that is somewhat explored in the philosophy of mind. But, I suspect what you're angling for is the notion that metaphysics without regard for real life experience and a bit of experimentation might be an exercise more in vocabulary and hubris than in genuine model building of reality, whatever that might be. A phrase like "grand and sweeping metaphysical framework" describes certain philosophical products of thinkers like Aristotle, Aquinas, Spinoza, Kant, and others to describe with completeness everything known. Such efforts find themselves championed by some and decried by others. A good example of the latter is the logical positivists who almost 90 years ago made a concerted effort to eliminate metaphysics by declaring it meaningless. Surprise, they failed.
Philosophies and philosophers whose methods lie heavily on introspection might be characterized as Cartesian, named after the somewhat infamous Rene Descartes. His views on mind-body duality still animate a lot of discussion about philosophy and thought, and Daniel Dennett coined the term Cartesian theater to push back against certain views. One view that is generally met with skepticism today is the idea that just because you think, and think you are, you can be certain of everything else. "Cogito ergo sum" is probably as contested as it is famous.1 Another conception of thought termed the analytic-synthetic distinction has also met with criticism by philosophical giants such as Quine, who attacked the idea in his Two Dogmas.
Is there a line between philosophy which problems are solvable by "pure thought" and which aren't?
Modern philosophers who have examined the question about distinctions in knowledge and problems that are either a priori or a posteriori, either rational or empirical, either synthetic or analytical have generally converged on a simple idea. There is no clear division between one and the other, a notion related to the sorites paradox, which suggests that nice, convenient, crisp categories are artificial linguistic artifacts, and that definitions and reasoning might be fuzzy or prototypical instead of being swept into tidy sets defined by simple intensions. So it's fair to say that a somewhat popular view of philosophy, that its a bunch of people "navel gazing" engaged in "pure thought" is a misconception. Daniel Dennett certainly knows more about science than Bill Nye knows about philosophy.2
1 - My intent here is to caricature Descartes obviously historical brilliance. Certainly he is one of the most influential Western philosophers by consensus. That his views on the pineal gland, the consciousness of animals, and his overestimation of the strengths of logic have not aged well do not undermine his obvious genius. He certainly didn't have access to empirical methods of epistemology that have laid bare the defeasibility of reason.
2 - My intent here is to goad shallow thinkers who think that science has somehow replaced or made irrelevant philosophy. The advancement of the methodologies of sciences is indebted to philosophy of science, even long before such a term was used. Bill Nye has since conceded his original views on philosophy were superficial (Quartz).
