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Ooooh finally my area of expertise! I don't know how humid Sydney is but I've done long runs in 38 degrees and 90% humidity. Wear a hat and sunglasses. Dry your shoes properly when you get back as otherwise they'll start to rot. Run as early as possible. You said there's a drinking fountain - if that's the case then you won't need to take any water, just drink water before you head out and have a pocari sweat (other sports drinks are acceptable, I guess, but I'm pocari4lyf) when you get back. Oh and wear sunblock, australian sun is vicious. There are loads of sports-specific ones available in Aus that don't sweat off quite as quickly, but you'll need to factor in putting it on and letting it set before heading out (and also don't put too much on your forehead or it will melt into your eyes).
On a very different note, we'll hopefully be in Sydney in Feb to see my wife's family. What do I need for 28ยบ long runs? A weird baby bottle thing? One of those jazzy little running caps?