J.B.
Check out this web page. I know the info is from Austin but it is only about 20 miles to Round Rock so I wouldn't think it would be too different.
http://weather.kvue.com/history/airport/KEDC/2009/9/5/Dai...
You can change the year on the search. Scroll down to the bottom and it breaks the temperature and humidity down by the hour. You can view September 5 2009-2011. I used September 5th because that is what day it was in 2011.
Hope this helps.