Solve the following sql problem:
What is the percentage of the units of item no.5 sold among all units of items sold in store no.3 on the day with the highest max temperature in 2012?

Schema:
SCHEMA:
- Table: sales_in_weather
  - Column: date
    - Samples: [2012-01-01, 2012-01-01, 2012-01-01, 2012-01-01, 2012-01-01]
  - Column: store_nbr
    - Samples: [1, 1, 1, 1, 1]
  - Column: item_nbr
    - Samples: [1, 2, 3, 4, 5]
  - Column: units
    - Samples: [0, 0, 0, 0, 0]
- Table: weather
  - Column: station_nbr
    - Samples: [1, 1, 1, 1, 1]
  - Column: date
    - Samples: [2012-01-01, 2012-01-02, 2012-01-03, 2012-01-04, 2012-01-05]
  - Column: tmax
    - Samples: [52, 50, 32, 28, 38]
  - Column: tmin
    - Samples: [31, 31, 11, 9, 25]
  - Column: tavg
    - Samples: [42, 41, 22, 19, 32]
  - Column: depart
    - Samples: [None, None, None, None, None]
  - Column: dewpoint
    - Samples: [36, 26, 4, -1, 13]
  - Column: wetbulb
    - Samples: [40, 35, 18, 14, 25]
  - Column: heat
    - Samples: [23, 24, 43, 46, 33]
  - Column: cool
    - Samples: [0, 0, 0, 0, 0]
  - Column: sunrise
    - Samples: [None, None, None, None, None]
  - Column: sunset
    - Samples: [None, None, None, None, None]
  - Column: codesum
    - Samples: [RA FZFG BR,  ,  ,  ,  ]
  - Column: snowfall
    - Samples: [None, None, None, None, None]
  - Column: preciptotal
    - Samples: [0.05, 0.01, 0.0, 0.0, 0.0]
  - Column: stnpressure
    - Samples: [29.78, 29.44, 29.67, 29.86, 29.67]
  - Column: sealevel
    - Samples: [29.92, 29.62, 29.87, 30.03, 29.84]
  - Column: resultspeed
    - Samples: [3.6, 9.8, 10.8, 6.3, 6.9]
  - Column: resultdir
    - Samples: [20, 24, 31, 27, 25]
  - Column: avgspeed
    - Samples: [4.6, 10.3, 11.6, 8.3, 7.8]
- Table: relation
  - Column: store_nbr
    - Samples: [1, 2, 3, 4, 5]
  - Column: station_nbr
    - Samples: [1, 14, 7, 9, 12]

SELECT CAST(SUM(CASE WHEN T1.item_nbr = 5 THEN units * 1 ELSE 0 END) AS REAL) * 100 / SUM(units) FROM sales_in_weather AS T1 INNER JOIN relation AS T2 ON T1.store_nbr = T2.store_nbr INNER JOIN weather AS T3 ON T2.station_nbr = T3.station_nbr WHERE T1.store_nbr = 3 AND T1.`date` LIKE '%2012%' AND T3.tmax = ( SELECT MAX(T3.tmax) FROM sales_in_weather AS T1 INNER JOIN relation AS T2 ON T1.store_nbr = T2.store_nbr INNER JOIN weather AS T3 ON T2.station_nbr = T3.station_nbr WHERE T1.store_nbr = 3 AND T1.`date` LIKE '%2012%' )