Heatwaves have always punctuated the Australian (and global) landscape, and occur due to the manifestation of numerous conditions, such as low rainfall, dry soil, higher than average background temperatures, and the positioning of what's called a "persistent high" - a near-stationary high pressure system that advects warm air to the area affected. They are measured relative to the local climate base period - so heatwaves can (and do) occur in Hobart, potentially resulting in catastrophic local impacts, even though the measured temperature would be cooler than a heatwave in Alice Springs.
By the description I gave above, it is completely plausible for heatwaves to occur in a stationary climate - one that is not showing any overall change whatever reason, other than year-to-year fluctuations due to natural cycles (e.g. El Nino/Southern Oscillation). So heatwaves did actually occur before human activity had any measurable impact on the climate system. If we assumed that the climate was stable around natural climate variability, we would not expect to see any increases or decreases in the number of heatwaves, their intensity, duration, or how early the first one occurs each season. Heatwaves themselves would still occur, but we wouldn't see any real change in their behaviour over timescales much longer than a few years.
However, measurable changes in heatwaves have occurred, which includes research I've undertaken myself here, here, and here, and that reported by the Intergovernmental Panel on Climate change.
But are we sure these changes are actually due to us? How are we sure they aren't due to natural causes? Such questions are indeed on the mind of many when we do actually experience a heatwave.
We need to be careful in what question we're actually asking. As I mentioned above, I constantly get asked "are humans to blame for this heatwave?". We cannot categorically answer this question, with a yes or no, or even with something like "humans were 75.3% responsible for the massive Australian heatwave in 2013". As I also said above, a range of factors need to be present for a heatwave to occur, including human-induced climate change.
But what we can determine instead is the changes in likelihood, or risk, that climate change has imposed on recent heatwave events. Using the example in the last paragraph, we can say something like "climate change has increased the likelihood of the massive Australian heatwave occurring in 2013 by 75.3%". This is saying that the event can occur without climate change, but occurs more often than it otherwise would have, due to climate change (note that 75.3% is a random number for illustrative purposes).
The difference between the two answers are subtle, yes, but very important.
Think if it like betting on a racehorse. There are numerous factors that influence whether or not a horse will win, likely including breed, training, age, track conditions, jockey, fitness, etc. The odds of the horse winning are controlled by these factors, that rise and fall based on their balance. Better training = better odds and poor track = worse odds, for example (although one might overshadow the other if they both occur at the same time). If the horse did win, we can't put it down to any one factor, and can only say, at most, that any one factor increased/decreased the odds, or likelihood of that win.
This logic applies when investigating the human influence behind specific events, such as heatwaves. So how do we do it?
This is where climate models come in. We only have one set of observations, and so climate models provide us with lots of data that include the affects of human activity (such as the release of greenhouse gases), and lots of data where only natural climate variability prevails. We can then compare how often heatwaves occur in this natural-only world, to how often they occur when our current level of human activity is present. This gives us our change in likelihood, or change in odds, due to human induced climate change.
To throw in another analogy, the same method is applied to understanding the likelihood of cancer in smokers. In fact, climate scientists stole this method from epidemiologists. The rate, type and severity of cancer is determined in large groups of smokers vs non-smokers. This allows for the estimation of by how much smoking increases your cancer risk, compared to if you didn't smoke at all.
And, unfortunately, though likely unsurprisingly, human activity has increased the likelihood of more intense and more frequent heatwaves. If we consider actual observed events, such as the intensity and frequency of heatwaves during the 2012/2013 Australian summer, human influence has more than doubled the likelihood (or doubled the odds) of events like these occurring. This means that heatwaves like those during the 2012/2013 season occur twice as often as they used to. It's important to remember that this is very different to stating that humans are (insert your favourite number here)% responsible for the heatwaves that occurred during this season.
So, in summary, we can certainly quantify the human signal in heatwaves. But in order to do this properly we need to be asking the right question.
If in doubt, think of the racehorses!