...And moving momentum along wires is something they probably can do pretty routinely, as this is probably how their inertial damping / artificial gravity works. At least in modern backstage doubletalk, that is: there exists a gravity generator at location X that moves gravity to the locations in need along suitable channels.
Is it unreasonable to set the ship's phasers to heat the area periodically?
That would depend on what the phasers could heat, how accurately, and to what sort of temperature.
Firing a hand phaser at a cleverly placed pile of rocks so that they attain the temperature of 1,500 degrees Celsius (so you get that nice red glow) is a good idea; the heroes can always find a comfortable distance at which to bask in the heat. Firing a starship phaser at an area of bedrock twenty meters across so that it attains the temperature of 1,500 degrees Celsius is not - finding a comfortable distance between the searing heat and the surrounding bitter cold is very difficult, since these things don't scale well, and there will be secondary effects, including whirlwinds that may suck in the poor survivors and turn them to cinder. The heated area will also probably be geographically quite exposed, in comparison with the small pile thing that can be set up anywhere, meaning the heroes will have well-done bellies and deep-frozen asses or vice versa.
The best option might be to carve a cave in which the heroes would be safe from wind chill and could retain the heat generated from hand phaser firing and from their own bodies. But a deep pit opening towards the sky would not serve well. It doesn't seem likely that the ship's phasers would have the precision to carve a more practical cave by firing from the horizon.
Getting things down from the ship to the planet will only help the castaways if these things directly protect them from more than a hundred degrees of deadly cold. Blankets or clothing or fuels will be of no help: what is needed is a hermetically sealed shelter such as a hut or a spacesuit, and those would kill the occupants if improper materialization damaged their life support mechanisms. If simple heaters fail, a spacesuit isn't going to work, either.
Timo Saloniemi
