How much time does Luke have?
Thanks to the diagnostic criterion of blue extremities and puffy skin, we can likely rule out Luke as being in the stages of moderate or severe hypothermia. Luke’s bewildered state and sluggish pace places him in the mild stage of hypothermia, placing the upper limit of his core body temperature at 35.0 °C (95.0 °F). This is also a reasonable starting point for the temperature of the tauntaun carcass, as it has been dead for several minutes.

With Luke’s body temperature decided, we can now determine how long it takes for the Jedi to plunge into severe hypothermia and with it, death. If Luke enters the tauntaun in a state of mild hypothermia, Han only has 17 minutes and 48 seconds to remove Luke, clean off the fluids from his face, and move him to warm shelter before moderate hypothermia sets in. The bigger scare here is the possibility of severe hypothermia, limb loss, and death, with Han having the extremely short window of 47 minutes and 26 seconds to extract, transport, and warm Luke.

Even if Luke is at a normal body temperature (37 °C/98.6 °F), Solo has just under 60 minutes before Luke plunges into the deadly realm of severe hypothermia.