Thank you for your query on Healthcare Magic.
Bluish discoloration of lips, hands, and feet as due to presence of cyanosis
and poor peripheral circulation.
The temperature that is low and it is called hypothermia
The bluish discoloration and low body temperature is due to decreased blood supply which usually occur in shock
and it is an emergency condition.
Persistent bluish discoloration is seen in congenital hear problems which are present since birth.
Some time heart rhythm abnormalities may present with such sudden features of decreased blood supply to the organs.
Some times a seizure
episode and breath holding spells will present sudden stop of respiration and bluish discoloration.
So consult your Pediatrician
for further evaluation.
Hope I have answered your query.