Yes, July is really hot so you're best to pack light. Korea has all four seasons, with summer being very hot and humid (sometimes quite rainy) and winter being quite frigid (with the occasional snow storm). Spring and fall are the most comfortable seasons for most people. Pack what you need for the season and keep it to a minimum. Remember, you'll eventually have to bring it all back with you, and I haven't met many people who don't take in the fantastic shopping opportunities in Korea.
What you'll need for:
Summer - Not much...t-shirts, shorts, a bathing suit, pair of pants and maybe a light jacket for cooler nights (which there aren't many of in the summer).
Winter - A good warm winter coat and a sweater or hoodie. The temperature does dip down to -15 or more at times so bring a few warm clothing items.
Spring and Fall - Think, warm days and cool nights. Bring your regular summer items with a light-medium density jacket for the cooler nights.
Keep in mind that you can buy pretty much anything in Korea at a decent price. Large size clothing or shoes are the only items that are a little more difficult to come by (but they are there).