Notes on Metaphor
Think "of" something. Think "through" something. The difference in the experience of the thinking here has to do with the underlying metaphor.
As Lakoff & Johnson explain in their book Metaphors We Live By, "The essence of metaphor is understanding and experiencing one kind of thing in terms of another."
When we say think 'of' something, or think 'through' something, we're experiencing thought as something with spatiality. The thing we think of suddenly exists for us in the mind as if it had real substance and dimensionality.
To think 'through' something means to think of it as though it's capable of being crossed, as though the thinking were a park you could walk through, or a door through which you entered into a room. There is a sense of a distance being traveled, a horizon crossed.
What it means to think 'of' something is, in my opinion, a much more difficult metaphor to understand, as 'of' can imply any number of different abstract relationships.
'Of' can express a relationship between a part and a whole (the finger of a hand) a measure and a value (40 pounds of pressure) a direction and point of reference (West of Texas) a cause and effect (died of cancer) And basically any correspondence between two categories or entities.
'Of' is very mysterious and versatile. When asked to think 'of' something, it usually means bringing the thing to mind, calling it forth as an object into the gallery of one's imagination.
Ultimately, depending on the way we say it, we will encounter whatever we think about in a unique way; unique to the properties of the metaphor we employ.