The reading of many editions of The New Testament is probably wrong in 2 Cor. 3.2. The reading “our” for what was written on hearts has to be the Corinthian hearts since it couldn’t be read on Paul’s heart by everyone.
The key conceptual proof is “Known and read by everyone.” If Paul wrote to his own heart people could not read his heart. He might tell others about the Corinthians with his heart stirred and the hearers could possibly infer some things, but that is not what the text seems to be saying. The better solution is that Paul’s preaching and interaction among the Corinthians impacted their behavior in such a way that others recognized the grace of Christ, who Paul preached, in the lives of the Corinthians.
The important Sinaiticus Codex however has “your” instead of “our.” Here is the text according to the Codex Sinaiticus:
Are we beginning to commend ourselves again? Or do we need, like some people, letters of recommendation to you or from you? You yourselves are our letter, written in your hearts, known and read by everyone. (2 Cor. 3.1-2)