a) not a very precise answer
b) maybe
c) maybe
d) not very effective nor practical
e) you don't have a lot of fluid to play with in a 2 y/o and 37C is too low
so b or c but "As the core reaches temperatures of 31°C or below, the body loses its ability to generate heat by shivering" so b not usefull
i'd say c
"Moderate rewarming methods provide heat at approximately 3°C/h. Methods include warmed gastric lavage (2.8°C/h), intravenous solutions heated to 65°C (2.9°C/h), and peritoneal lavage with 45°C fluid at 4 L/h (70 kcal/h or 3°C/h).
Rapid rewarming methods provide heat at levels higher than 100 kcal/h.
Methods include thoracic lavage at 500 mL/min (6.1°C/h), cardiopulmonary bypass (400 kcal/h or 18°C/h), thoracic lavage at 2 L/min (19.7°C/h), and warm-water immersion (1500 kcal/h).
In comparison, endogenous shivering provides rewarming at a rate of 300 kcal/h.
No noninvasive technique rewarms as rapidly as full-body immersion in warm water. Known as the Hubbard tank technique, immersion has successfully rewarmed humans with severe hypothermia.
Unfortunately, patients who require rapid rewarming in the emergency department also need cardiac monitoring and intravenous therapy, both of which are difficult to manage under water.
Defibrillation also is difficult; however, defibrillation likely is futile once a patient's core temperature falls below 30°C."