An airbag module for a motor vehicle includes a gas sack that can be inflated with gas to protect an occupant, a gas generator for generating the gas provided for inflating the gas sack, and an additional cooling device comprising an openable reservoir for storing a coolant. The reservoir is opened when the gas sack is inflated, so that the coolant for cooling the gas used to inflate the gas sack can come into contact with the gas. The cooling device comprises a movement generating device that opens the reservoir to release the coolant.