Tie into the moribund warmth (4,4)
I believe the answer is:
dead heat
'tie' is the definition.
(dead heat is a kind of tie)
'the moribund warmth' is the wordplay.
'the moribund' becomes 'dead' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'warmth' becomes 'heat' (synonyms).
'dead'+'heat'='DEAD-HEAT'
'into' is the link.
Can you help me to learn more?
(Other definitions for dead heat that I've seen before include "Produce tie" , "A shared first place" , "Where runners are equal first" , "two are inseparable here" , "Tie for first place in race" .)