Paul’s outburst of thanks (we also thank God continually; see also 1 Thessalonians 3:9–11) is a reflection of his deep awareness that God was at work in the Thessalonians and that he is worthy of our constant gratitude for his gracious working in our lives. Such an awareness would naturally come to expression at appropriate points in the course of a letter; it need not be restricted to formal thanksgiving sections.
In addition, by expressing his gratitude in this way, Paul encouraged the faith of the beleaguered Thessalonian believers by reminding them that their faith was not a delusion but the work of God himself. As I have argued, this is the main thrust of 1 Thessalonians 2:1–13.
13 And we also thank God constantly for this, that when you received the word of God, which you heard from us, you accepted it not as the word of men but as what it really is, the word of God, which is at work in you believers.