In 100 years: they should be about the same temperature-wise, but 5-10" wetter.
For each normal period, average temperature in January/July/Annual and then annual precipitation (deg F and in)
1921-1950 19.1 / 73.0 / 46.6 // 30.00 (warmest normals, warmest summer and winter)
1931-1960 18.0 / 71.1 / 45.3 // 30.16
1941-1970 16.8 / 70.1 / 44.9 // 30.25 (coldest normals, coldest summer)
1951-1980 15.6 / 70.6 / 45.2 // 30.84(coldest winter)
1961-1990 16.0 / 71.0 / 45.2 // 30.88
1971-2000 17.3 / 71.6 / 46.1 // 32.95
1981-2010 18.8 / 71.3 / 46.4 // 34.48
2081-2110 23.8 / 74.3 / 50.2 // 45.06 (linear extrapolation from 1941-1970)
2081-2110 18.3 / 68.5 / 46.1 // 41.95 (linear extrapolation from 1921-1950)
Edit: Found images of the long-term temperature, snowfall, precipitation, etc
at this site.
The diurnal range probably didn't change as much as it looks. Data was taken in the city (early years) and airport in later years. Before 1896 temperatures were only recorded at 7am, 2pm, and 7pm so the max/min wasn't always the true value.
Except for a few extremely wet years in the early 1880s, most of the wettest years have been recent.
Snowfall has been up since the 1950s or so. 2013-2014 had about 60" of snow, 2014-2015 had a little under 30".
Temperatures have stayed similar and so has the
annual maximum temperature, but the
heating degree days have trended downward,
annual minimum temperature has been milder as of late, and the average ice cover at the largest lake in Madison (Lake Mendota) has decreased steadily: