Staying warm is one of the single most important problems facing a human being. If it were not for the need to stay warm, I believe few people would fear homelessness. There are only a limited number of strategies available to keep the cold at bay.
You can dress warmly. Wear lots of layers. Wear thermal underwear during winter. Wear more than one pair of socks at a time. If you are in a place that gets down to 30 or 40 degrees fahrenheit, wear earmuffs and wear warm gloves. The thermals are available in department stores. Try Target or Walmart first, Sears, JC Penney, and others after, to get them at the lowest available prices. Gloves and fleece earmuffs will be there too. For other layers at a discount price, try wearing multiple undershirts or check with Goodwill and Salvation Army for cheap, warm clothing. If even that is out of budget, an old hobo trick is to stuff your clothes with crumpled newspaper. It does help.
I always had three blankets in my car during winter, and one was always a Mexican, loosely woven blanket. The loose weave leaves air spaces that make for good insulation. The other two can be any inexpensive cotton, fleece, or poly blend you like. I avoid wool, because although it is an exceptional insulator, itchiness is simply unacceptable. You may disagree, particularly in freezing climates.
An astronaut's mylar blanket is always handy, too. They only cost a couple of dollars and can usually be found in army surplus stores and sporting goods stores in the camping section. Wrapped around you, they retain 95% of your body heat by reflecting it back at you. You can save less heat, but be more comfortable, if you simply place the mylar between a couple of other blankets. One of the problems with mylar is it can get slick with condensation from your body's sweat, and that is unpleasant and can cause a chill. If they're thin blankets, I recommend you fold the mylar sandwich all together, to make it easier to get ready for bed the following evening. The slickest way is to fold the blankets in half once and roll it like a sleeping bag.
Stores supplying camping gear will also have hand warmers. These chemical pouches run a couple of dollars a piece, but it is handy to have a few for particularly cold moments. You can optimize their value by using them under a mylar blanket.
Another great source of heat is a hot water bottle (usually available in drugstores). Buy a propane stove, again available in camping supplies for under thirty dollars. You are going to want one to cook with anyway. Propane bottles are about two dollars each and last quite a while. Boil some water and fill the water bottle before you find your final parking spot for the evening, so that neighborhood busybodies are not tipped off to your presence. Wrap the bottle in a towel to avoid leaks, or at least place a towel under it. Leaks will happen without warning. Boiling water is hotter than the rubber bottle is designed to take, but for the bottle to work most of the night, it has to be boiling. The leak will happen as it cools, and it will be slow. I never got burned by a leak, but caution is in order while filling the bottle. Scalding is a hazard. I usually went through two bottles per winter.
When all else fails, you can make sure the exhaust pipe of your car is not under the car cover, and run the engine and heater for a while. It is a giveaway that you are there, of course, but there are few people about on a cold night. I took the chance quite a lot some winters.
That is about the whole list, unless you want to get a steel barrel and start a fire in it. Best to do that on the outskirts of town.