Frank has temperature following terrible cold (6)
I believe the answer is:
direct
'frank' is the definition.
(similar in meaning)
'temperature following terrible cold' is the wordplay.
'temperature' becomes 't' (abbreviation).
'following' means one lot of letters go next to another.
'terrible' becomes 'dire' (synonyms).
'cold' becomes 'C' (eg on taps).
'dire'+'c'='direc'
't' put after 'direc' is 'DIRECT'.
'has' is the link.
(Other definitions for direct that I've seen before include "Instruct" , "Outspoken" , "Candid" , "without ambiguity" , "Control the affairs" .)