Kerrits do fantastic 'performance tights' that are super light weight and great in summer- take a bit of getting used to though as you feel naked! In Australia we get days in excess of 40 degress Celcius aka **** HOT! And these breeches make it so much more pleasant to cope with, particularly if teaching and riding a number of horses in the day.
I also agree with smrobs re the long sleeved shirt vs tank top. I can't stand riding in tank tops, not only is it the sunburn factor, but you have the direct sun on you making you hotter, and if you come off you can take a lot more bark off your arms than if you're wearing long sleeves or a t-shirt. I try to wear very light cotton 3/4 length button up shirts in summer to keep the sun off me but let the breeze through.
It's also tempting to wet yourself down a bit - but don't! It gives relief for a few minutes and then it makes you even hotter! - Same goes for horses, people hose them off then put them out, but the water heats up and forms a hot layer around the horse's body, scrape the water off before you put them out!