Dull morning following temperature close to heatwave (4)
I believe the answer is:
tame
'dull' is the definition.
(I've seen this before)
'morning following temperature close to heatwave' is the wordplay.
'morning' becomes 'am'.
'following' means one lot of letters go next to another.
'temperature' becomes 't' (abbreviation).
'close to' suggests the final letters (the 'close' to the word).
The final letter of 'heatwave' is 'e'.
'am' put after 't' is 'tam'.
'tam'+'e'='TAME'
(Other definitions for tame that I've seen before include "quiet" , "Subdue" , "Submissive -- pedestrian" , "Domesticated, gentle" , "Not exciting; domesticate" .)