Thinking Mind is concerned with ideas and knowledge in their own right
What Sri Aurobindo calls the Thinking Mind would seem to be equivalent in part with Cognition in Faculty Psychology, and the Jungian "thinking" or "intuitive thinking" faculty i.e. thinking primary and intuition secondary (Thinking Type).
The following further quotes of Sri Aurobindo are from the "Divine Plan" website (no longer online)
A well-trained intellect is a good preparation of the mind for greater knowledge, but it cannot itself give the yogic knowledge or know the Divine - it can only have ideas about the Divine, but having ideas is not knowledge. Intellectual activities are not part of the inner being - it is the outer mind.
To see the Truth does not depend on a big intellect or small intelllect. It depends on being in contact with the Truth and the mind silent and quiet to receive it. The thinking mind with most men is, in matters of life, only an instrument of the vital.
An architect of knowledge, not its source.
This powerful bondslave of his instruments
Thinks his low station Nature's highest top.