Early stage shoe's warmer (4,4)
I believe the answer is:
heat pump
'warmer' is the definition.
(device which warms something up)
'early stage shoe's' is the wordplay.
'early stage' becomes 'heat' (early stage of a sporting contest).
'shoe' becomes 'pump' (pump is a kind of shoe).
'heat'+'pump'='HEAT PUMP'
(Other definitions for heat pump that I've seen before include "Mover of energy from cold to hot region" , "Device used in fridge" .)