Yeah, it can, and has always been. The hottest it's gotten in Australia is in my State (South Australia), 50.7 °C (123.3 °F), which was recorded (2 January 1960 at Oodnadatta) which is well north into the interior of the country from the capital of Adelaide. It get's humid down here too, but not often, that's the domain of the northern parts of the country from Broome to Darwin and across to Cairns.
We have heatwaves too, but it's common place. I've been in the UK during one of their heatwaves, (2018), with temperatures around 28-30 and it was terrible, for the reason you mention, no AC.
I tend to get grumpy when it's hot for long periods, it's just irritating. Walking outside is like walking into an oven (from the AC inside) and I don't feel like doing anything. Most people here feel the same I guess, as with you folks up there.