Not quite sure what you mean by default template but if it's the template defined by qnew then you either go to the registry or use Interop as shown:
AcadApplication InteropApp = (AcadApplication)Autodesk.AutoCAD.ApplicationServices.Application.AcadApplication;
string template = InteropApp.Preferences.Files.QNewTemplateFile;
Database db = new Database(false, true);
db.ReadDwgFile(template, FileOpenMode.OpenForReadAndWriteNoShare, true, "");
If you know the template name then InteropApp.Preferences.Files.TemplateDwgPath; would get you the path