I think that the Gospel of Thomas shows awareness of Pauline themes, and perhaps even Paul's letters.
Let's begin with Logion
Now some may sneer, saying that this quotation is simply the same quote from Isiaha, which Paul utilizes. Some may also say that it reflects a common tradition between Thomas and Paul, while others may suggest that it is a genuine quote from Jesus which Paul reminds his audience of, and Thomas retains. Two the latter suggestions, I need only reply that an extant written source is generally preferred to a hypothetical written/oral source, so it is the safest to say that it is directly Pauline.
Now to the former objection, it is unlikely that Thomas would quote from the Scriptures, because he holds some distate for Judaism and LXX Christians. Let us look at Logion 52:
His disciples said to him, "Twenty-four prophets have spoken in Israel, and they all spoke of you." He said to them, "You have disregarded the living one who is in your presence, and have spoken of the dead."
In keeping with the grouping of sayings in Thomas, this Logion is followed by another anti-Judaic saying:
53. His disciples said to him, "Is circumcision useful or not?" He said to them, "If it were useful, their father would produce children already circumcised from their mother. Rather, the true circumcision in spirit has become profitable in every respect."
Now here Jesus seems to reflect a paulinist tradition about the 'true circumcision of the heart.' Although this Logion exchanges spirit for heart, the pauline tradition is apparent.
Back to Logion 52--the dead--we can postulate that other references to 'the dead' may have the Old Testament in mind. Earlier on in Logion 11 then: Jesus said, "This heaven will pass away, and the one above it will pass away. The dead are not alive, and the living will not die. During the days when you ate what is dead, you made it come alive. When you are in the light, what will you do? On the day when you were one, you became two. But when you become two, what will you do?"
As a final note, in no other case does Thomas quote from the LXX.
Another possible allusion to Paul would be Thomas' use of Adam as a prototypical character. Adam is central in Paul's explanation of his soteriology in Romans. For instances, in Logion 85, Jesus states:
"Adam came from great power and great wealth, but he was not worthy of you. For had he been worthy, he would not have died." We certainly have the idea that Adam was a failure before God.
Perhaps we have some recourse to Adam in the Book of Jubilees, but it is difficult to tell how popular this book actually was. In any case, I need to develop this better. These are just some ideas.
But it seems here that Thomas knows at least 1st Corinthians and possibly Romans, or even Galatians.