Cross Republican states in extremes of temperature (8)
I believe the answer is:
traverse
'cross' is the definition.
(synonyms)
'republican states in extremes of temperature' is the wordplay.
'republican' becomes 'r' (abbreviation).
'states' becomes 'avers' (I've seen this before).
'in' indicates putting letters inside.
'extremes of' suggests removing the centre.
'temperature' with its middle taken out is 'te'.
'r'+'avers'='ravers'
'ravers' going into 'te' is 'TRAVERSE'.
(Other definitions for traverse that I've seen before include "Go across" , "Ski diagonally across (a slope)" , "Move across" , "get across" , "Extend or bridge across" .)