A sterilization container has a valve arrangement that remains open in a venting phase and is then closed before a pressure difference is compensated for at a predetermined differential pressure. The valve remains closed until the container is opened for the purpose of withdrawing and using the sterilized instruments contained therein. The valve is actuated through a snap disk arrangement, the snap disks of which vault gradually into opposite directions at predetermined temperatures, thereby effecting a defined valve control. The snap disk arrangement is provided in a thermally isolated housing, which prevents a premature back-switching of certain snap disks that could be caused by a cooling-off as a result of the evaporation of condensate.