DWT templates are obviously used in AutoCAD, because that's the software that was used to make these in first place. Once you use them for making new content, you can export it to any supported format you desire.
It is unlikely any 3rd party software can re-purpose .dwt files, so in context of dwt to stp conversion, your only option is AutoCAD itself. Export to STP format is often done to export the geometry for 3D print or to act as exchange format.