James Hansen pointed out long ago (eight years? more?) that the variance of the PDF of temperature difference from climatological average increases, not just the central location.
(In layman's terms: not only is the bell-shaped curve shifting over to the right, it's also getting squashed down flatter and wider.)
So you don't just get proportionately more extreme weather events: you get a lot more than that. As well as many, many more extreme heat-related events, we can expect to see extreme cold events at a similar rate as in the past (or perhaps slightly more of them). Like Texas's this year.
I think this point is not widely appreciated.