Dynamic Pivot Results to a Temp Table

You should be able to use INTO Clause. I added INTO into your example.

SET @cols = STUFF((SELECT distinct ',' + QUOTENAME(QT.QUESTION_DESC)
                 FROM #QUES_TEMP QT
                 GROUP BY QT.QUESTION_DESC
                 FOR XML PATH(''), TYPE
                 ).value('.', 'NVARCHAR(MAX)')
                 ,1,1,'')

set @query = 'SELECT EVAL_ID, AuditType, ' + @cols + ' from
        (
            select     QT.EVAL_ID,
                       QT.AuditType,
                       QT.SCORE,
                       QT.QUESTION_DESC
            into ##tmp
            from #QUES_TEMP QT
         ) x

        pivot
        (
             max(SCORE)
             for QUESTION_DESC in (' + @cols + ')
        ) p '

execute(@query);

SELECT * FROM ##tmp