When I use pandas read_csv to read a column with a timezone aware datetime (and specify this column to be the index), pandas converts it to a timezone naive utc
The answer of Alex leads to a timezone aware DatetimeIndex. To get a timezone naive local DatetimeIndex, as asked by the OP, inform dateutil.parser.parser to ignore the timezone information by setting ignoretz=True:
import dateutil
date_parser = lambda x: dateutil.parser.parse(x, ignoretz=True)
df = pd.read_csv('Test.csv', index_col=0, parse_dates=True, date_parser=date_parser)
print(df)
outputs
Temperature
DateTime
2016-07-01 11:05:07 21.125
2016-07-01 11:05:09 21.138
2016-07-01 11:05:10 21.156
2016-07-01 11:05:11 21.179
2016-07-01 11:05:12 21.198
2016-07-01 11:05:13 21.206
2016-07-01 11:05:14 21.225
2016-07-01 11:05:15 21.233