A Russian here. Don’t. You aren’t trained for this. Go to any place that is open 24/7 and, worst case scenario, spend the night walking. Sleep during the day.
If you get a sharp stubbing pain in your fingers, toes, or (less likely) cheeks, immediately take off your glove or sock or what have you and massage the part that is hurting. Massage until circulation is restored, i.e. until it’s red. Rubbing with snow is a good way to restore circulation. It’s counterintuitive, but you want to shock your capillaries into expanding. No circulation = no oxygen for your cells = necrosis. Warm blood circulating will warm you up.
If you were Russian and were dressed adequately for the weather and know how to do the above, I’d recommend spending the night exercising. Exercise will keep you warm. That’s how my grandfather survived evacuation to Siberia in a cattle train during the WW2, by chopping firewood with an axe. Others who were more passive didn’t survive.
The car will keep you warm but also humid. Too many variables there.
Warm shoes, socks, gloves, a hat are a neccessity.
If you are staying warm by burning candles or other things, get a carbon monoxide/smoke detector.
If you have access to firewood, consider burning fire all night. Get a bunch of reflective thermal blankets (you can get them in a dollar store) and make a shelter out of them near the fire. But you can’t sleep.
I think police would be your best bet, by far. Don’t be a hero, don’t brave it.
If you can’t afford to leave the engine idling all night with the heater blowing (and the tailpipe carefully down-wind of your sleeping chamber), then a quality sleeping bag is the ticket.
Once zipped up in a sleeping bag, your own body heat will keep you warm inside that padded cocoon.
Shed as many clothes as you can before you climb into the sleeping bag, and keep your shoes and boots OFF. Clean socks on your feet are paramount.
If you can’t afford a sleeping bag, then construct a sign and stand near the entrance of the nearest Walmart or sporting goods store. Ask for help in getting yourself a sleeping bag, and explain your situation.
Some nice person like me will surely come along, and purchase one for you.
How do I know this?
Because I have bought them for homeless people before.
Photo courtesy of iStock.

Go to a gas station that is within a highway service center, where regular traffic comes almost non stop. There is usually a McDonald’s or Burger King and a Convenience store there, and you’ll see many truckers making sleep stops.
Park in the main parking lot and keep your car running with the heat on as deisired. Keep charging your phone because if your state has an anti idling law there is usually a clause that allows your car engine to remain idling as long as it is being used as a power source for something (I.e. charging electronic devices). When you get to about 1/4 take of gas, drive your car over one of the pumps and idle there with the heat on. Wait for people to come who are filling their own tanks.
Go up to each and every one of them and say “Excuse me, sir/ma’am, can you help me? I am homeless and I a few gallons of gas to keep my beginning running so I do not freeze to death out here. Could you spare 8 or 9 dollars to get me a few gallons of gas?”
say this to everyone, it will work about 1/4 of the time. Repeat the process until you have a full tank of gas. There are many good caring people in this world who want to help those in need, and you are not asking too much of each of them.
if you run your engine with the heat on constantly you will need about one and half tanks of gas per day. Thankfully the highway will never stop delivering potential donors. All you have to do is ask nicely and be honest about your needs. Have no fear, if one says no, the next one will say yes.
Find a hotel with a public restroom, preferably a nice hotel with complimentary breakfast. Depending upon the area don your best vacation clothing (business, weekender, wedding, you get the point) and do your best to look like you belong there.
Find a restroom with stalls (more than one is best so there are no complaints about not being able to use it) and post up there until you can safely leave in the morning. If you are really good you might be able to get in on breakfast.
I have spent 25 years in the hotel business. This is easily done if you have the clothing to fit in. If they think you are a guest you are practically untouchable. Staff is trained to accommodate your every need and whim. That includes unusual sleeping arrangements and odd waking hours. Advice: don’t bring a lot into the hotel with you. Look like a guest, not a homeless person.
GO SOUTH!
Okay, maybe that’s not an option…
I’ve slept in the bed of my truck at -25F.
On top of the metal of the bed, I had a thin foam mat. And I had a fleece liner in a kick-ass sleeping bag. (It was rated down to -30F.) I think I may have put a few more blankets underneath me on those cold nights.
I woke up in a cocoon of ice — I nearly froze to death when I had to get out and pee.
So, make insulation. Paper, plastic bags — if there’s any leaves, pine needles, or long grass around, bag that shit and fill the cavity of your cave, tent, lean-to, car, whatever with them.
Put on all your clothes. Layers are your friends.
And make your car into a nest, pack the insulation around you so you won’t suffocate yourself, and get comfy. (If you do a good job, you’ll want to leave the window cracked.) You’re a mammal and a primate — and adept at making nests — make yourself a kickass nest, like your life depends on it. (It does.) Pretend you’re a polar bear making a den. Pretend you’re a beaver — whatever — they’re our cousins, ya know?
When it’s that cold, insulate, insulate, insulate. Keep your space small, and you likely won’t need to run the heater, nor an external heat source. But if you have sun — store that heat in the thermal mass of your insulation. Your car is a solar oven. Don’t let that precious heat get away! Again, leaves, shredded newspapers, shredded cardboard, etc — in bags or boxes — woody things with air gaps hold heat well, and will release it throughout the night.
If this is what you’re committed to doing, and there’s really nowhere else to go…
Don’t let yourself get down. It’s an opportunity to be creative and to challenge yourself. Don’t be stupid — get as many blankets or the best sleeping bag you can afford — and insulate well around yourself.
Heat rises. Insulate up.
Have a back-up plan if you realize you are stupid. (I’ve had stupid moments. Found myself out in some forest trying to start a fire, shivering in the dark at 2:00 AM — hands were shaking too much to get a fire started. Truck was too cold to start and I didn’t want to kill the battery. That sucked.)
If you find yourself shivering too much, do something or go somewhere to get some warm liquids — or just go warm up in some 24-hour business place. (I like to think businesses aren’t always assholes when it’s that cold.) But save up enough money for as much hot coffee as you can afford — sit out the night and drink coffee indoors. I used to work a lot of night shifts. Night shift people are usually pretty chill.
In the day leading up to it, ask small business people if you can sweep their sidewalk or take out their trash for a cup of cocoa or coffee…be a good person.
Stay warm, my friend — stay warm.
…and be sure to clean out your nest when it warms up. Living like a wild animal is only okay for the short-term.