Heat is a game mechanic which essentially limits the amount of intensive activities a ship can perform in a given period of time. The amount of heat that a ship currently has is displayed in the Heat Indicator. Each module has a percent of Power usage (can be seen in the Modules subpanel on the right) which indicates relatively how much heat it will generate when it is being utilized. Each activity that is performed (boosting, shooting, etc.) as well as being in certain environments (close proximity to a star) will increase the heat in a ship and once the heat is greater than 150% the ship's hull will begin to take consistent damage.
A Cobra MkIII with cooling vents releasing heat.When rigged forsilent running, these vents close.
To cool a ship off the player can equip Heat Sink Launchers which will allow the player to instantly dissipate some of the ship's built up heat or by upgrading the ship's Power Plant heat will be dissipated more efficiently which means that the ship will not overheat as quickly.
A higher amount of heat will also increase the ship's Signature which means that the ship will be more easily detectable by other ships in the area. If a ship has no heat (generally all modules have been turned off) or is in Silent Running mode (all heat is trapped in the ship) then it will be undetectable by other ships unless they are close enough to visually see the ship.
A sidewinder releases heat by opening its coolant vents.