A sterilization container for medical instruments includes a receptacle with a bottom wall and an open top, there being a multiplicity of vent openings in the bottom wall. The receptacle has a cover movable between a closed position wherein the cover closes the open top of the receptacle and an open position wherein the cover is positioned to allow access to the interior of the receptacle. A filter sheet is positioned in the receptacle so as to cover the bottom wall and the vent openings therein and the receptacle contains one or more trays for supporting medical instruments above the filter sheet. A perforated highly thermally conductive plate is positioned between the trays and the filter sheet so that when steam enters the container through the vent openings during steam sterilization, it heats the plate to a temperature sufficient to revaporize steam condensate collecting on the plate. The internal structure of the container is also disclosed.