Overheat is a game mechanic that has first apperared in Revenge of the Yolk. It's been added to prevent the player from constantly holding the fire button.
On the top left of the screen near the score counter is the overheat bar. When the bar is filled, your weapon will overheat. This will prevent you from firing until it cools down, which takes 5 seconds. Missiles do not depend on this mechanic, so they still can be fired while this is in effect. Collecting any kinds of power-ups will instantly deplete the overheat bar and remove its effects.