Earlier quoted context omitted.
It's not that hard... you just throw some ice packs in the groin and armpits. You won't get them fully into the TTM range in a 20 minute transport, but you can start the process.
That is extremely ineffective. What you might want to do is to cool the brain through cooling the outside of the head as well as through the nasal cavity. Even if you chug a giant slurpee the largest effect on the brain temperature will be the cooling of the nasal cavity on it's way down.
We're talking about a naked, sedated patient (so they're already losing a lot of heat due to simple convection, and there's no heat being generated by skeletal muscle movements). The body's metabolism has slowed significantly, and it's producing anywhere near the normal level of "baseline" heat.