Was this betta just purchased? The poor buggers are usually very unhealthy when you buy them due to being kept in cups, etc.
Are you using a quality water treatment/dechlorinator such as Seachem Prime? There's other good ones out there too.
I'd skip the salt and concentrate on keeping the water changed. You should have an API master test kit to allow you to measure for ammonia, nitrite and nitrate in PPM. Test strips are OK as backup and a rough idea of what you've got going on.
Warmer water will help speed along bacterial or parasitic issues, but something viral or otherwise it won't help.