If your data is in a parameter called weatherData
then the largest temperature value will be
Max[weatherData[[All,2]]]
If you have Mathematica version 10.1 you can also use TakeLargestBy
to get the largest value for temperature along with the associated date.
TakeLargestBy[weatherData,Last,1]
That 1 in the expression tells TakeLargestBy
to only give you the largest value. If you want more of them then change it to another integer.
Of course if your list has more than one date with the same largest value then you will only get one of the values.