I would say it's a philodendron, one of the 'pink lady' varieties. It does look kind of like a peace lily (spath), but those don't have aerial roots, which a see a couple of, and also what appear to be stems. First thing is to hydrate - it's severely wilted. Take the whole thing, pot and all (remove the drainage saucer if you can), and dunk it into the sink or tub filled with hot water. Hot water works very well to quickly revive over-dry plants. And I mean really hot, as hot as your hands can stand. Let it soak for a couple of hours, then let it drain for a couple more. You can cut off the dead brown parts now, if you want - you can tell the dead parts, they'll be crispy. I wouldn't do anything else to it until it has recovered from the shock of being in a desert for who knows how long. It should start to stand back up, at least many of the leaves should, though you'll probably have a number of leaves that will turn yellow and ugly. You can cut these off, they will eventually become crispy anyway. When you cut them, cut the leaf stem from the main stem flush with the main stem. At this point, you can go ahead and repot according to the number of good suggestions to be found on this forum, or ask again for more help with repotting

I would wait to do any repotting until the spring or early summer just to be safe. The warmer temperatures will make for much better conditions for new root and plant growth. I do grow my Hoya DS-70 in a clay pot and it does just fine but it is watered almost every day, still clay is best used for species that like to dry out vs the moisture lovers. Having temperature drops at night are good for plants, many bloom in response to these types of conditions. The temperatures you mentioned are not ideal but they are not low enough to cause problems. If you are concerned about fertilizing then I would suggest waiting for the most favorable conditions. On a nice sunny day water the plants and then apply your fertilizer solution. This is the best approach when it comes to watering any plant that is sensitive to water during the winter. Mike

construction site, dug this guy out from under a large rock, in pretty bad shape. Does anyone know what I have here? Thanks in advance.

No repotting into bigger pot pls. In 2 years, plant should be bigger and/or have some pups. Does the whole pot feel heavy? Leaves seem to be water-logged. It looks like it is in soil that retains water, and there is possibility that it could be rotting. If my plant, I would take it out of pot and get all soil off the roots. Take clear photo and post for us to see their condition.