You can print opened .vstm templates as PDF documents, however this would you no good. This is because templates are just blank documents with saved settings to quickly create new documents based on predefined specifications. So yes, you can make this conversion, but it's pointless to make it.
Convert Microsoft Visio 2013 macro-enabled template file to Adobe Portable document format.
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert vstm to pdf on Windows
A vector based diagramming software from Microsoft
Convert from vstm file format
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.