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Well, regarding the daily mean, the hottest day of the year on average is on August 5th with 18.4°C (65°F).
And the coldest day of the year is on February 14th with a daily mean of 0.9°C (33.5°F)
Still have to calculate the average of the hottest and coldest days.
Warmest day on average in the period of 1949-2013 is 30.8°C / 18.8°C (87/66°F)
And the coldest day on average: -5.2°C / -10.3°C (23/13°F)
Of course this has varied over the past 65 years, but the trend shows a gradual rise in the temperature of the hottest days.
This is especially noticable at the number of days with tropical nights (nights with a minimum above 20°C/68°F).
While these were the exception until the Mid90s and the very first tropical night was recorded 20 years after the DWD station starts recording in 1949, they have become quite common nowadays occuring almost every year.
Also the number of days surpassing the 30°Cs mark has risen considerably and while until again about 1990 the mercury does not rose much above 31 or 32°C on the hottest days, these days 33 and 34°C degrees have becoming quite common and since 2010 we had a 34+ degree (except for 2011) in every year. Probably only a question of time until the alltime heat record of 35.8°C of August 1992 will be broken.
My best guess is for the coldest, somewhere in the 20s. The absolute coldest temp is usually in the upper teens, with a high around freezing that day typically. The hottest day is usually in the 90s, but it still drops to around 65 at night, so I'll call it 80.
In a given year on any day:
Hottest: 22°C/40°C, mean of 31°C
Coldest: 2°C/10°C, mean of 6°C
On average, (1970-present):
Hottest: Feb 06, 14.4°C/27.4°C, mean of 20.9°C
Coldest: Jul 10/11, 5.2°C/12.8°C, mean of 9.0°C
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