Nobel-laureate economist Paul Krugman lays out a simple demonstration of how an increase in the global average temperature necessarily leads to more extreme weather events without eliminating other effects:
Now suppose that a warming trend shifts the whole probability distribution to the right — which is what we mean when we talk about climate change. Then the result looks like this:
What happens is that the right tail gets fatter: the probability, and hence the frequency, of extreme events goes up.
Two immediate implications. First, there will still be cold stretches: global warming shifts the distribution, it doesn’t eliminate the left side of the distribution. So there will still be cold spells; that proves nothing.
Second, no individual weather event can properly be said to have been "caused" by global warming. Heat waves happened 30 years ago; there’s no way to prove that any individual heat wave now might not have happened even if we hadn’t emitted all that CO2.
But the pattern should have changed: we should be getting lots of record highs, and not as many record lows — which is exactly what we do see. And we should be seeing 100-year heat waves and similar events much more often than history would have suggested likely; again, that’s what we actually do see.
The point is that the usual casual denier arguments — it's cold outside; you can’t prove that climate change did it — miss the point. What you’re looking for is a pattern. And that pattern is obvious.
Shortly later Krugman pointed out that China, historically a net food exporter, has to import food this year because of record droughts.