As the chart (right) shows, there are two trends. First, the peaks of the data-based curves move right, over time, with respect to the reference curve. In other words, the average temperature is rising. Second, more recent curves are flatter. A flatter curve means a bigger standard deviation and a wider spread of results.
If the mean of each curve were the same, such flattening would imply both more cold periods and more hot ones. But because the mean is rising, the effect at the cold end of the curves is diminished, while that at the hot end is enhanced. The upshot is more hot periods of local weather.
Moreover, the bell-curve method makes it possible to say just how much more hot weather there is. Dr Hansen defined extreme conditions as those occurring more than three standard deviations from the mean of his reference curve. In that curve, this would be an eighth of a percent at each end, which is more or less the value in the curve for 1951-61. Nowadays, though, extreme conditions (or, at least, those that would have been considered extreme half a century ago) can be found at any given time in about 8% of the world.