Overheat is a feature that first apperared at Chicken Invaders: Revenge of the Yolk.
Since the game featured automatic fire for the first time in the series, Overheat was created to prevent the player from constantly holding the fire button.
At the top left of the screen, right next to the score, is the Overheat bar. When the bar becomes full, your weapon will overheat. This will prevent you from firing for a few seconds. You can still fire missiles or Super-secret Mine Bombs. Using any weapon upgrade will automatically cancel overheat.
To prevent Overheat, just take smalls breaks from firing every few seconds.
Firing manually overheats weapons much slower. Since firing manually also means firing faster with some weapons, it's clear that it is much better to fire these weapons manually.