Apparently mild hypothermia only sets in when the body temperature has fallen at least 2 degrees C below normal. This source doesn't say anything about convulsing or flopping around uncontrollably (are you describing shivering?) but it says moderate hypothermia is from at least 5 degrees C below normal and severe hypothermia-> death becomes a risk at 9 below normal.
https://my.clevelandclinic.org/health/diseases/21164-hypothermia-low-body-temperature
Hypothermia, or low body temperature, is a condition that occurs when your body’s temperature drops below 95 degrees Fahrenheit (35 degrees Celsius). The average normal body temperature is 98.6 F (37 C).
Mild hypothermia
Mild hypothermia means your body temperature is between 95 F and 89.6 F (35 C and 32 C). Signs of mild hypothermia include:
Shivering and chattering teeth.
Exhaustion.
Clumsiness, slow movements and reactions.
Sleepiness.
Weak pulse.
Fast heart rate (tachycardia).
Rapid breathing (tachypnea).
Pale skin color.
Confusion and poor judgment/loss of awareness.
Excessive urination.
Trouble speaking.
Moderate hypothermia
Moderate hypothermia means your body temperature is between 89.6 F and 82.4 F (32 C and 28 C). Signs of moderate hypothermia include:
Slow down in breathing and heart rate.
Slurred speech.
Decline in mental function.
Hallucinations.
Decreased shivering.
Bluish color to skin (cyanosis).
Increased muscle stiffness.
Dilated pupils.
Abnormal heart rhythm.
Decreased blood pressure.
Weakened reflexes.
Loss of consciousness.