Left relatives outside with the furnace (4)
I believe the answer is:
kiln
'furnace' is the definition.
(I know that kiln is a type of furnace)
'left relatives outside' is the wordplay.
'left' becomes 'l' (common abbreviation).
'relatives' becomes 'kin' (kin can mean relatives or family).
'outside' is an insertion indicator.
'l' put into 'kin' is 'KILN'.
'with the' is the link.
(Other definitions for kiln that I've seen before include "Large oven, for potters say" , "Oven for burning lime" , "Oven for hardening and drying" , "Furnace, oven" , "Pottery-firing oven" .)