There is a limited amount of covered seating in lower level seats on the first base side of the field. Almost all of these seats are found in the 100 level sections that are located directly behind Sections 11-38. So instead of sitting in Section 38, look for seats in Section 138 or an adjacent section in the 100s.
Within these 100 level sections the higher the row, the better the chance of being covered. Closer to home plate, as many as 7 or 8 rows are covered and will keep you cool. But as you move further down the lines away from home plate, only the last row or two are protected. In Section 138, for example, only row 39 is completely covered.
For additional recommendations on staying cool in the afternoon, check out Where is the best afternoon shade at Globe Life Park?