The best fit for the data above would be a 5th degree polynomial. Because the shape displayed in the two charts is not the same, it is clear that Degree Days don't preserve the true weather/load relationship, which indicates an essential loss of information.
For a long time, Degree Days may have been the best option available, due to limited availability of hourly data. Fortunately, this is no longer the case. There are over 1,000 stations in the publicly accessible NOAA system that record hourly data and most have records going back 20 years.
With the present availability of hourly data we shouldn’t be using a method of information shorthand that is a holdover of a bygone era. Hourly temperatures themselves are not the solution to creating better weather analysis, but once hourly data becomes the basis for that analysis, there is the possibility option to use an advanced approach.
Read my next post about how hourly data allows us to use non-linear models.