We do not need to spend much time in the rest of the Paul's letters, because there is little racial teaching in these 3 books. We shall summarize the little that there is.
Thessalonica was (and is today) a city on the Greek mainland, west of Philippi. It was a major trade and political center, linking the Balkans to Greece. Paul visited the city once, during his second missionary journey (about AD 49). This was just after he and Silas were beaten at Philippi. His reception at Thessalonica was not much better. There were enough Jews in the city to form a synagogue, and Paul went there to preach about Christ:
Some of the Jews were persuaded and joined Paul and Silas, as did a large number of God-fearing Greeks and not a few prominent women (Acts 17:4).
But not all that starts well ends well. Luke recounts that jealous Jews stirred up a local mob to seize Paul and Silas. When they couldn't find them, they grabbed a man name Jason, who had let the apostles stay at his house. They brought him before the local officials, but Paul and Silas got out of the city by night (Acts 17:10). Eventually, Paul went on to Athens.
Paul wrote two letters to the Thessalonians, and they were among his earliest epistles. They were written around 50-52, possibly from Corinth, where Paul stayed after he left Athens. The second letter was a quick followup to the first one.
Timothy may be considered Paul's Gentile protege. He not only rated two letters in the New Testament from Paul, but a mention in many other books (Acts, Romans, 1 and 2 Corinthians, Philippians, Colossians, 1 and 2 Thessalonians, and even Philemon and Hebrews!). It would be a fascinating study just to reconstruct his life.
We know from Acts that Timothy lived in Lystra, a city in south-central Asia Minor. His mother was Jewish, his father Greek. Paul apparently had great plans for Timothy, because he had him circumcised (Acts 16:3). This from the apostle who later vociferously opposed the circumcision party. But Paul must have intended for Timothy to have a ministry that extended beyond the limited circle of Gentile converts, and circumcision gave him credibility with and access to both Jews and Jewish believers. Timothy travelled with Paul in Greece and Asia Minor, and after Paul had been imprisoned in Rome, he asked him to come there (2 Tim 4:21). The first letter was written to Timothy in Ephesus (1 Tim 1:3), from Macedonia, around 63-65 AD. The second letter was written from Rome, shortly before Paul's execution, 66-67 AD.
There is no racial teaching in these books.