Extremes

Why would the number of extremely hot days rise by a much larger percentage than the rise in average temperatures?

It's to do with the shape of the statistical distribution.  Let's suppose that the average temperature for a season or a year is X, and that the observations are normally distributed.  That means that the number of times  the temperature is X-10, X-9, X-8 ...... X+8, X+9, X+10 (just as an example)  starts out with very few times it's X-10 (or X+10), a few more times when it's X-9 (or X+9), still more times it's X-8 (or X+8), in a shape which is reminiscent of a bell.  The normal distribution is often called the bell curve because of this.

There are other distributions which are skewed to one end of the curve or the other, which means that they are asymmetrical.  For example, wealth is very asymmetrically distributed: there are far fewer rich people who own most of the wealth, and lots of poor people who own little.  But observations for weather tend to be symmetrically distributed, but because of global warming, they have drifted over time.  The distribution is still bell-shaped but the mean  (the average) has shifted higher.  And that means that the "tails" of the bell shape have also shifted.  So whereas in the old days you had say 1 very hot day 3 days a year, 1 % of the time, now you have 2 or 3 or 4 times as many very hot days.  Similarly, in the old days you used to get 1 very cold day 3 days a year, now you get none.  The graphic below demonstrates this principle very nicely.

Source

Lots of people think that a rise of 1 degree C in average temperatures is small, because they are used to the shifts in temperature from day to night, and from winter to summer, which are obviously much larger.  But what global warming means is that we will have far more hot days in summer, with temperatures reaching and exceeding new highs more often and by more.  We have just seen this in our Australian summer, and they've just seen this in the US, where February heat has been at July levels,  If the mean, and its whole distribution shifts still higher the number of super hot days will double or treble or quadruple, with devastating consequences for us and for our world.