it may be her teeth moving in her gums if she hasnt cut any yet or teething again?
I would give her some panadol and see if the temp comes down and she settles ....if the temp goes to 38+ then yes take her to gp .
Temp is 36.5 to 37.5 so i wouldnt worry to much just yet ... if she doesnt drink at all for up to 6 hours ( im saying 6 as there is at least two feeds in 6 hours ??) then a gp visit is the next option. Sounds like teeth and the warm weather.
YOur doing the right things keep a/c on nice temp strip her down to nappy and singlet. 37.7 isnt too warm if she hits 38.1 then panadol nd if temp doesnt budge then gp . I do know these things as i work with peads in emergency and the amount of time mums think the kid has a temp they dont ... beleive me 37.7 isnt a worrying figure ok ...