How can one find out how many days per year a city x experiences a temperature of less than y degrees at time z of the day?

WeatherSpark solves your problem ("do I need a warm jacket?") perfectly. Go to their page for Seattle, then click on September and you get this wonderful chart:

As you can see, if you travel to Seattle on Sep 1st, night time temperatures get down to 14 degrees. If you want to dive deeper and ask about 8pm specifically, the next chart can do that as well:

This tells you that temps stay above 18 degrees until roughly September 22nd and you should expect cooler weather after that. Not "exact temperatures" but this is as good as it gets, short of downloading public weather datasets.

If you do wish to download and parse data on your own, you can use the Mesowest service for US measurements. After making a free account, you will be able to download data for 1 year/month at a time. In 2020, the lowest temperature at 8PM in September was 56F/13C according to that dataset. If you want to get data for more years, you'll have to write a small script to download/parse multiple CSVs or make use of their public API.

Padmanabha Chowdhury pointed me to:

All the climate data of US are available on the National Climatic Data Center, under the National Oceanic and Atmospheric Administration (NOAA). You can get county, city or state based rainfall, wind etc. data of both recent and historical times.

Data link: https://www.ncdc.noaa.gov/cdo-web/search

E.g. to answer the question how many days per year Seattle experiences a temperature of fewer than 10° C at 8 p.m., using the freely available NOAA data:

Data file (bug: all hours are given, not just 20:00):

Notes:

• I've added col E to get celsius, formula: =ROUND(CONVERT(D2,"F","C"), 1).
• FYI: Meaning of columns from NOAA documentation (mirror)

To only keep 20:00: open in Notepad++, replace regexp (?!^.*T20.*$)^.+\r?\n with empty string (if one wants a different time, change T20 with e.g. T05 for 5 AM):

Plotting temperature at 20:00 in Celsius vs. day:

Converting day# to readable days: https://www.calendar-365.com/day-numbers/2021.html

The temperature change over days is very smooth because the given temperatures are average. From the NOAA documentation (mirror)

This is the aggregation of the value for a particular date and time, plus and minus 7 days, over each of 30 years.

and https://www.ncdc.noaa.gov/cdo-web/datasets#NORMAL_HLY:

Hourly climate normals are computed for the 30 year period from 1981 to 2010 for U.S. stations (usually airports). Values include temperature, dew point temperature, sea level pressure, wind direction and speed, and other climate probabilities and statistics.

(which explains why earlier we could only select 2010 as the year when selecting which data to download)

Data check: JonathanReez? wrote:

In 2020, the lowest temperature at 8PM in September was 56F/13C according to that dataset.

Same in NOAA data.

Same plot for midnight: