The Deep Thinkers are a group of Baron Klaus Wulfenbach's counsellors who have only rarely been mentioned in the comics ✣ so far. By implication, they help the Baron develop his long-view strategies and study the ripple effects of actions reported to them. Whether they are normal humans, high-order clanks or heads in jars of extraordinary thinkers preserved at last minute is unknown at this point.
In Agatha H and the Clockwork Princess (footnote 61, p. 326) they are identified as the surviving(?) result of Sparks who, on identifying their own limitations as one of the reasons for the failures of their schemes, focus on enhancing their own intelligence (instead of their psychological failings, basic inability to grasp reality, or such). They are considered useless for day-to-day planning, but useful for correlation of vast amounts of data for prediction and influence of future trends and outcomes.
Kleegon the Battlemaster was originally dubbed "Deep Thinker" by fans, appearing aboard Castle Wulfenbach, functioning as a strategist and an advisor.
Update: We now have more support to believe the strategists on Castle Wulfenbach are indeed Deep Thinkers as they are used to review the military maneuvers ✣ suggested by Tarvek.