A lot of it isn't the kilt as much as everything else. I prefer to wear the lightest weight hose I can find, and a poly-cotton uniform shirt. I've got one by Horace Small called "Tropic Aire"; it's supposed to be made for tropical climates, to wick moisture away and breathe, which it does much better than my cheap polyester band shirt. A lot of guys wear poly-cotton polo shirts; you can find them at Highland games with embroidered clan crests. Avoid 100% polyester shirts, Jacobite shirts, and wearing a waistcoat and jacket as much as possible (heaven forbid a doublet & full piper's plaid!). If I must wear a jacket, I leave off the waistcoat unless going formal.
Some of it is also situational awareness; I always know where the closest shade is, and whenever possible I'm standing in it.
Hydrate, hydrate, hydrate.