^ It is if you assume there's nothing a faster-than-light starship can do to stop it from happening. And have you ever experienced minus-40? I have, wearing a full winter suit, and I couldn't stand it. The notion of someone wrapped in a blanket, laying against a rock, at
negative-117, is absolutely ludicrous. At that point, Sulu should have already long-since been dead anyway. It looked so fake, like someone had no idea what arctic-like conditions would be like.
And they can't at least have Spock say "we tried airdropping shelter kits unsuccessfully; they all landed over 12 kilometers away". Instead, the Enterprise just circles above, fretting because the transporters don't work. Forget shuttlecraft. The notion that the crew was that helpless and Sulu and his boys are doomed is ridiculous. The notion of anyone having any life left in them at all at that temperature is over-the-top fake.
If you look at the plot, they could've used a similar situation without saying "117 below" and showing Sulu and company struggling, without making it so ridiculous. So, as I see it, there were three ways (hindsight being 20-20) to make this ep more rational.
1: Spock tells Kirk the Enterprise takes a chance by air-sropping shelter-kits, but the kits miss the target by, say, 12 KM. Sulu and company opt to stay put, but the storm drops temps to 0˚ C. They use phasers on rocks, but a crewman is injured carrying rocks to the camp site.
2: Let's assume it gets a little colder than 0˚ C. Let's say that it's -10˚ C or -20. Spock air-drops the shelters, but only one lands nearby. Others are too far away. Everyone tries to take turns in the shelter, but a crewman on the surface is injured carrying rocks to the site for phaser-heating. This provides a little more realistic jeopardy, and shouldn't affect the budget.
3: Alright, let's assume that Alfa 177 does indeed get to -117. At this level of danger to the expedition, the Enterprise crew should be resourceful enough to find a way to air-drop shelters off-camera. You can assume the shelters reach the target. Instead of showing Sulu using a phaser, we see Sulu and his team happily reporting to Spock that the airdrop worked; we see Sulu on the surface and a parachute flapping above the rocks behind him. We don't need to see the shelters. From then on, we hear Sulu report on the radio of how they're all cramped in the shelter-capsules, and one of his team was injured in the wind storm. They're alright, being kept warm by body heat. But one of his men needs medical attention. This allows the team to face danger without it being over-the-top silly or fake-looking.