There are costumes that are heavier, and costumes that are lighter. Many costumes have less clothing, such as ones that are sleeveless, or incorporate shorts. If you have a costume that covers more of the body, you can try to use lighter fabrics, such as linen or super thin cotton.. One costume that my husband likes is a pilot from Battlestar Galactica, because they wear a double tank top, which leaves arms bare. I have a Daenerys costume from Game of Thrones that is light and sleeveless. But my TWD Carol costume is heavy and has a jacket and knee boots, which makes it too warm for recent SDCCs.
My husband and I debuted Orville costumes last year, which are unfortunately warm, because of the jackets. But we got breathable 'hiking-style' black t-shirts to wear underneath that wicked away a lot of body heat, and that helped a lot. As an extreme, you can always wear some kind of cooling packs underneath your costume.