The gist of Heat is that you're all crooks who want to steal as much as possible while not drawing too much heat from the fuzz. (That's the current lingo, yes?)
The game lasts three rounds, and each round starts by players drafting a hand of five cards, with them then playing cards four times over the course of a round.
To play cards, everyone chooses a card from their hand and reveals them simultaneously. Most cards feature a single letter — A, B, or C — and the cards resolve in this order, with all the As, some of which are shown above, taking effect first.
The B cards take effect next, and most of them involve you "earning" money in some manner, with money being represented by colored chips. When you take heat, you remove the red cubes from the heat chart starting with those in the bottommost row and you place them in front of you, perhaps smugly self-assured that you are indeed a bad person because you now have evidence of it.
The C cards take effect last, with many them being concerned with who has heat. You don't want heat, but if you're doing something illegal, you're probably going to get it. Such is the nature of a life in crime — or at least a life playing card games that pretend you have a life in crime.
Some cards feature two letters, and they do something at each of the appropriate times. They're pretty straightforward.
The numbers and heads at the bottom of each card instruct you as to how many players can handle the intensity of a Mastermind (five is too many) or Lay Low (three is not enough) or Backup Plan (four is just right).
If you can't take enough heat from the chart because you've already claimed it all, everyone who can returns one heat and pays $3. You've gotta pay people off to help you hide out, yes? If you instead use the APB mini-expansion, some of which is shown above, you draw one of these cards and something else happens.
After three rounds, everyone with heat loses money for each heat cube they have, with each cube costing the amount of the largest empty row on the heat chart. After settling your debts and paying still more people for their silence, whoever has the most money wins!