E seems awkward.

From my personal standpoint I don't see how it can be a fact that it is possible it can serve as a themomter. It either does or it doesn't. Otherwise it is not a fact.

Not sure if that is the correct reasoning tho.

In English Language.
USE: TO ATTRACT.
OPTION A.
'For attracting females rise and fall in accordance with the surrounding temperature ,and they can in fact serve'
'for attracting'? we have better options of 'to attract' thus this option is incorrect.
Option B.
'for attracting females rises and falls in accordance with the surrounding temperature,which can in fact serve'
'for attracting' this makes the option incorrect,i would rather go for better options.
OPtion C.
'in attracting females rise and fall in accordance with the surrounding temperature, in fact possibly serving,
This option looks like a possible answer to the question but it lacks something which is the use of 'rise and fall' a temperature 'rises and falls'
thus this option is incorrect
Option D.
'in attracting females rises and falls in accordance with the surrounding temperature, in fact possibly serving',
THIS IS THE CORRECT OPTION.
IT FULLY CONVEY THE HEART OF THE MESSAGE IN SIMPLE WELL CONSTRUCTED TENSE AND IT FOLLOWS PARALELISM

OPTION E.
' to attract females rises and falls in accordance with the surrounding temperature, in fact possibly serving'
This option is incorrect.
'in fact possibly serving' is a conditional statement