Son more sick, with temperature, raises support (7)
I believe the answer is:
trellis
'support' is the definition.
'son more sick with temperature raises' is the wordplay.
'son' becomes 's' (genealogical abbreviation for son).
'more sick' becomes 'iller' ('ill' can be similar in meaning to 'sick').
'with' means one lot of letters go next to another.
'temperature' becomes 't' (abbreviation).
'raises' says the letters should be written backwards.
's'+'iller'+'t'='sillert'
'sillert' written backwards gives 'TRELLIS'.
(Other definitions for trellis that I've seen before include "Support for creepers" , "Structure supporting climbing plants" , "latticework in the garden" , "Garden climbing frame" , "Framework - stiller (anag)" .)