There is a local myth concerning the name "La Luz" that says in pioneering days the villagers would light a bonfire every night that could be seen in Tularosa, indicating the villagers were safe from marauding Indians - no bonfire was supposed to signal people in Tularosa of the need for armed help. So yes, there is a great panoramic view from the village elevation out over the desert.
As for the name of the town, it's a bit more mundane. By some accounts it was founded by Franciscan friars as early as the early 18th Century and called Nuestra Señora De La Luz (Our Lady of the Light).
There is not going to be significant temp differences. There is an outdoor concert series on the parking lot of the Space Museum in the summer that is comfortable most evenings once the sun drops below the horizon, but can be uncomfortable earlier.