As far as I know, I did think is more emphatic than I thought, it means I really thought, I took time to think about smt.

When using a construction like "did + verb" in English, the speaker is adding emphasis - stressing that the action really happened. This might be said in response to someone who has implied that it did not happen. EXAMPLE: A: "I don't think you thought about going to the movie at all." B:"I did think about it, all day" -or- "I DID! I thought about it all day" Without "did", the sentence "I thought about going to the movie" is a simple statement and is more commonly used, unless an emphasis is needed.

I think "I did think" is used to emphasize that you actually thought on the subject and you are not only saying that u thought about it.