My favorite for summer purses are by Isabella Fiore (if you are looking for designer). The designs are more nature-based in the summer and use the colors of the season. You could also try a fun tote or woven bag that looks fresh and light for summer and allows you to pack a lot in it if you are vacationing.
Hot colors: Red, yellow, white and pink. You can go with the classic black, too. I like over the shoulder bags, because they're loose and more comfy in the heat.
Pick a lighter fabric in bright colors for the spring and summer. Consider a canvas purse that's washable if you get it dirty outside. Hobo styles look great in lighter weight fabrics.