You can use a simple mathematical formula to compress a month to a season, e.g.:
>>> [month%12 // 3 + 1 for month in range(1, 13)]
[1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 1]
So for your use-case using vector operations (credit @DSM):
>>> temp2.dt.month%12 // 3 + 1
1 3
2 3
3 3
4 4
5 4
6 4
7 4
8 4
Name: id, dtype: int64