As far as I know , SQLite does not support EXTRACT() function.
You can try strftime('%d', Timestamp)
psql.sqldf('''SELECT
  Timestamp
, strftime('%d', Timestamp) AS Day 
, Temperature
, Humidity
 FROM df
 ''')
Consider the below example which demonstrates the above query:
Example dataframe:
np.random.seed(123)
dates = pd.date_range('01-01-2020','01-05-2020',freq='H')
temp = np.random.randint(0,100,97)
humidity = np.random.randint(20,100,97)
df = pd.DataFrame({"Timestamp":dates,"Temperature":temp,"Humidity":humidity})
print(df.head())
            Timestamp  Temperature  Humidity
0 2020-01-01 00:00:00           66        29
1 2020-01-01 01:00:00           92        43
2 2020-01-01 02:00:00           98        34
3 2020-01-01 03:00:00           17        58
4 2020-01-01 04:00:00           83        39
Working Query:
import pandasql as ps
query = '''SELECT
      Timestamp
    , strftime('%d', Timestamp) AS Day 
    , Temperature
    , Humidity
    FROM df'''
print(ps.sqldf(query).head())
                    Timestamp Day  Temperature  Humidity
0  2020-01-01 00:00:00.000000  01           66        29
1  2020-01-01 01:00:00.000000  01           92        43
2  2020-01-01 02:00:00.000000  01           98        34
3  2020-01-01 03:00:00.000000  01           17        58
4  2020-01-01 04:00:00.000000  01           83        39
you can get more details here to get more date extract functions, common ones are shown below:
import pandasql as ps
query = '''SELECT
      Timestamp
    , strftime('%d', Timestamp) AS Day 
    ,strftime('%m', Timestamp) AS Month 
    ,strftime('%Y', Timestamp) AS Year 
    ,strftime('%H', Timestamp) AS Hour 
    , Temperature
    , Humidity
    FROM df'''
print(ps.sqldf(query).head())
                    Timestamp Day Month  Year Hour  Temperature  Humidity
0  2020-01-01 00:00:00.000000  01    01  2020   00           66        29
1  2020-01-01 01:00:00.000000  01    01  2020   01           92        34
2  2020-01-01 02:00:00.000000  01    01  2020   02           98        90
3  2020-01-01 03:00:00.000000  01    01  2020   03           17        32
4  2020-01-01 04:00:00.000000  01    01  2020   04           83        74