Do you have short sleeved dress shirts? Have you considered them?
Short sleeves are great for summer time, they are not as hot as a long sleeve yet give the appearance of still being very smart when worn with a sports coat, perhaps in a board meeting or for work.
They can transition from business, with a tie, to casual, with no tie. Short sleeve shirts can also be worn with shorts for a light summer look.
You can have just as much fun with them as long sleeved shirts, playing with all the same details; pockets, no pockets, buttonholes, thread colors, monograms.
Try one this Summer Season!