The Doctor has already come to terms with Turlough's alien nature with remarkable quickness. He also seemingly discovers the true nature of Turlough's mission with equal ease, which actually makes the events to come much more interesting.
While in Turlough's room, The Doctor finds Turlough's little glow cube that the boy has been using to communicate with the Black Guardian. A look of extreme consternation comes over The Doctor. Does he know what the cube is and what it stands for? Since he tells the Brigadier that they have to immediately find Turlough, you would think that The Doctor doesn't understand that Turlough intends to kill The Doctor.
Yet what does The Doctor do when he finds the boy? He gives him the cube back. The Doctor could have effectively severed the link between Turlough and the Black Guardian by destroying or discarding the cube, but instead, in returning the cube, he keeps Turlough bound to his contract with the Black Guardian. Is it The Doctor's (unspoken) intention to see this Turlough/Black Guardian arrangement through to its completion? Does he feel it's the only way to defeat the Black Guardian, as well as save Turlough? Only time will tell, but it would almost make The Doctor seem foolish if the audience knew what Turlough was planning while The Doctor didn't.