How can I calculate annual average temperature from a daily timeseries datasets of multiple stations for different hydrological year separately in R?

Question

I have a daily time series data sets in the following format:

df <- data.frame(Date = c("01/01/1950", "01/02/1950", "12/31/1975"),
                 MeanTempStn1 = c(13, 4.6, 9.8), 
                 MeanTempStn2= c(9.5, 3.8, 8.2), 
                 MeanTempStn3= c(10.8, 6.7, 5.5)) 

Date	MeanTempStn1	MeanTempStn2	MeanTempStn3
01/01/1950	13.0	9.5	10.8
01/02/1950	4.6	3.8	6.7
....
12/31/1975	9.8	8.2	5.5

I know how to get the Annual Mean for each station separately using hydroSTM with one code. But I need to calculate the Annual Average Temperature for each station separately for each hydrological year which starts on 01 September of each year and ends on 31 August next year. For example, the hydrological year 1976 starts 01 September 1975 and ends on 31 August 1976. How can I do it in R?

Any help would be deeply appreciated.

Thank you.

Best regards, Mohammad Hasan