His fins certainly -do- look odd, but it might not be fin rot...Some bettas fins curl and twist up like that when having had to deal with bad water quality like that (heck, some curl like that "just because", too, but I'd be willing to bet the poor quality for sure has had some effect here...). Aquarium salt, as was mentioned, sounds like a great idea, because it does look like some "clumping" going on...hopefully that'll help. Make sure to keep his water very clean and yes, get it warmer if you can, as soon as possible. That will help him heal. His tail also looks a bit frayed, which I suppose -could- be rot, or it could be him chewing on himself for nourishment, which I have seen many times. When my old boy Bishou went blind suddenly, due to disease caused by my newbie self two years ago, he started chewing on his tail. Chunks of tail would be missing, but it wouldn't have that "melted" look that is associated with rot...
Either way, clean water, warm temperature, and food every day should heal him right up if the damage done isn't too severe, outside of his body AND inside...