After reading the posting from @Shea Burns, I found another way.
If you had already installed both VS 2013 and the 10.3.1 SDK; then you can do the following.
Copy the following into the same paths for vs 2015 (Microsoft Visual Studio 14.0):
Microsoft Visual Studio 12.0\Common7\IDE\ItemTemplates\CSharp\ArcGIS
Microsoft Visual Studio 12.0\Common7\IDE\ItemTemplatesCache\CSharp\ArcGIS
Microsoft Visual Studio 12.0\Common7\IDE\ProjectTemplates\CSharp\ArcGIS
Microsoft Visual Studio 12.0\Common7\IDE\ProjectTemplatesCache\CSharp\ArcGIS
Microsoft Visual Studio 12.0\Common7\IDE\Extensions\ESRI
Follow step 4. from @Shea Burns.
Then run these command from cmd.exe (https://msdn.microsoft.com/en-us/library/y3kkate1.aspx )
devenv /installvstemplates.
devenv /setup.
Then you just have to make sure that all your assemblies are compiled to 4.5.0. You will get the following error if you forget to change your version.
" The "ValidateAddInXMLTask" task failed unexpectedly."