Get some coolers. They have lids. Don't try to heat the water: if it cools off some, it helps the fish survive (not safe below 62). Move fast, and have an airstone rig to handle all of them. Corals likewise. You can keep them in a rubbermaid Brute---or your qt tank for several days in the apartment with a bubbler while you handle the tank move. Have Prime on hand.
Discard the sand, get some new live sand (which I understand doesn't have to be washed) and set up asap in the new digs. Most modern apartments use rebar and foamed concrete for floors, so ok on that.
Expect that about 5 days after re-start, the 'new' tank rig will have a mini-cycle, which will soon be over. If you can keep the livestock in the Brute until that's sorted itself out, all should be well.