There Is No Such Thing as Conscious Thought (an interview with philosopher Peter Carruthers). Carruthers makes some very thought-provoking points. Well worth reading.
Or does he??!! 
I’ll have to disagree with Carruthers.
His argument works pretty well as a reduction ad absurdum of the theories of consciousness that he examined.
He spends part of that argument on the question of whether there are conscious thoughts. But that is not the same as the question of whether there is conscious thought. We can be conscious of the process (i.e. thought), without being able to individuate into discrete components (thoughts).
I would be inclined to the view that there is conscious thought but there are no conscious thoughts.
I don’t think there is much to be gained in this area. Calvinists would say “Fine”. Soft Calvinists would say “Maybe”, and everyone else would say “Nobody can prove that.”