TSQL Delete All dates and stores data
If I understand it right, these queries should work:

DELETE X
From BigTableX X 
Left join TempTableX T on X.PostingDate = T.PostingDate 
    and X.Store = T.PostingStore and X.SKU_id = T.SKU_id
Where T.Sku_id is null
AND EXISTS (Select 1 from TempTableX WHERE postingDate = X.PostingDate) 
AND EXISTS (Select 1 from TempTableX WHERE PostingStore = X.Store) 

DELETE X
From BigTableX X 
CROSS APPLY (Select TOP(1) p = 1 from TempTableX WHERE postingDate = X.PostingDate) P
CROSS APPLY (Select TOP(1) s = 1 from TempTableX WHERE postingStore = X.Store) S
Left join TempTableX T on X.PostingDate = T.PostingDate 
    and X.Store = T.PostingStore and X.SKU_id = T.SKU_id
Where T.Sku_id is null


Either of these 2 queries will delete the same rows.

On my test sample they are more efficient but my test tables don't match your data and you will have to test it.
They all do 4 table scan but the new query does not sort data (no DISTINCT). 

Can you please provide both execution plans (old and new query) for further analysis.

It may help to add an index on postingDate and on postingStore or on postingDate/postingStore/sku_id. If CLUSTERED INDEX on TempTable (Date/Store/SKU_id) is not narrow enough (3 varchar...), it may be better to remove it.