How to calculate maximum and minimum mean monthly temperatures?
From my experience, first of all, you should calculate the hourly average, in your case should be the average of the 2 minimum and 2 maximum temperatures. (In your sample data you need the 0:00 hours of 2009-05-02, as it is covering 23 hours)

Once you have the average by hour in a day, you can go for the daily average, then monthly average and so on...

For the minimum and maximum, there is no average, it should be just one value. If you want to calculate a monthly minimum average, then it should be calculated with the same process, so there is just one minimum by hour (the minimum in the range, f.e. 0:00-1:00), then one average of all the hourly minimums to get the daily minimum, and the same system for the monthly one.

If you try, you will see that you don´t have exactly the same result than making a daily average. For your sample, the daily average by hour is 26.31 degrees and by the daily average of all data is 26.25 degrees.

Hope it helps!