A 2007 paper on Observed Poleward Expansion of the Hadley Circulation since 1979 explains why southern Australia is so dry and hot now. The Hadley Cell is delivering its hot dry air 2.5 to 4 degrees further towards the poles than it was in 1979, which is 275km to 440km further south.
Basically, global warming increases heat at the equator and makes more moist air rise higher, faster than before (the water condenses as the air rises and you get lots of rain in the tropics). The air then moves southward toward the poles, and cools, so it falls back to ground level, recompressing as it falls – thus heating up – and delivering hot dry air to the ground. Melbourne is about 37 deg south, Sydney is about 33 degrees.