The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
2. Use UNION ALL instead of UNION (query line: 75): Always use UNION ALL unless you need to eliminate duplicate records. By using UNION ALL, you'll avoid the expensive distinct operation the database applies when using a UNION clause.

Optimal indexes for this query:

ALTER TABLE `#TEMPTABLE1` ADD INDEX `temptable1_idx_fld_storagegroupid` (`fld_StorageGroupID`);
ALTER TABLE `#TEMPTABLE2` ADD INDEX `temptable2_idx_fld_storagegroupid` (`fld_StorageGroupID`);

The optimized query:

SELECT
        SUM(CYJEWELRY) 'CY_Jewelry',
        SUM(CYAPPLICANCE) 'CY_Appliance',
        SUM(CYCELLPHONE) 'CY_Cellphone',
        SUM(PYJEWELRY) 'PY_Jewelry',
        SUM(PYAPPLIANCE) 'PY_Appliance',
        SUM(PYCELLPHONE) 'PY_Cellphone' 
    FROM
        (SELECT
            COUNT(*) AS CYJEWELRY,
            0 AS CYAPPLICANCE,
            0 AS CYCELLPHONE,
            0 AS PYJEWELRY,
            0 AS PYAPPLIANCE,
            0 AS PYCELLPHONE 
        FROM
            #TEMPTABLE1 
        WHERE
            (
                #TEMPTABLE1.fld_StorageGroupID >= 3 
                AND #TEMPTABLE1.fld_StorageGroupID <= 14
            ) 
        UNION
        SELECT
            0,
            COUNT(*),
            0,
            0,
            0,
            0 
        FROM
            #TEMPTABLE1 
        WHERE
            #TEMPTABLE1.fld_StorageGroupID = 1 
        UNION
        SELECT
            0,
            0,
            COUNT(*),
            0,
            0,
            0 
        FROM
            #TEMPTABLE1 
        WHERE
            #TEMPTABLE1.fld_StorageGroupID = 2 
        UNION
        SELECT
            0,
            0,
            0,
            COUNT(*),
            0,
            0 
        FROM
            #TEMPTABLE2 
        WHERE
            (
                #TEMPTABLE2.fld_StorageGroupID >= 3 
                AND #TEMPTABLE2.fld_StorageGroupID <= 14
            ) 
        UNION
        SELECT
            0,
            0,
            0,
            0,
            COUNT(*),
            0 
        FROM
            #TEMPTABLE2 
        WHERE
            #TEMPTABLE2.fld_StorageGroupID = 1 
        UNION
        SELECT
            0,
            0,
            0,
            0,
            0,
            COUNT(*) 
        FROM
            #TEMPTABLE2 
        WHERE
            #TEMPTABLE2.fld_StorageGroupID = 2
    ) A