Change site to SSL, Article Manager search stopped working
It's been years since we've looked at any of that code. But here's some tips and possible paths to explore:
The way Article Manager resolves "Server Side Includes" is by saving a temp file on the server and then requesting it back through the web server. This is why you're seeing those temp files. The code that does this is in the function _server_resolve_ssi_and_code() in /cgi-bin/artman2/modules/IT/SSIResolver.pm.
For debugging purposes, you can set this to 0 (from 1) at the top of that file to prevent temp files from being erased:
$ERASE_TEMP_FILES = 0;
The script requests the temp files from the URL specified in an internal variable named SERVER_RESOLVED_SSI_TEMPDIR_URL which is set to the value of "publish_url" from the artman settings.
So the first thing I'd check is that your https and http paths point to the same files. So https://www.example.com/news/publish/temp_1490792407.shtml and http://www.example.com/news/publish/temp_1490792407.shtml point to the same file.
Hope that helps!