I was out of town (with no internet access 8O ) when you started this thread, and there was no "betta" in the title to catch my eye!
Bettas, when stressed, tend to get finrot. The faulty heater was probably the cause. Bettas are most definitely stressed over fluctuating or cool temps. I have a spare heater just in case one of mine breaks.
Jungle Fungus Eliminator always worked wonders for me. Don't be afraid to give a second course of treatment if necessary, with the Kanacyn or the Fungus Eliminator. Even though finrot is usually bacterial, the Fungus Eliminator has an antibiotic in it too.
Kanacyn worked well for me too. I have always had good results with BettaMax, or if the finrot is more advanced, Kanacyn or Jungle Fungus Eliminator. So, if you're using Kanacyn now, it says to give a treatment every other day, for 3 treatments in 5 days. After 3 more days, you can repeat the full course of treatment. I would do a water change every other day too, before you give that dose for the day. Example -- on Monday, dose 1. On Wednesday, water change and then dose 2. I think the for this med,you're supposed to go the full 5 days with no water change. But since your betta hasn't gotten better, I think water changes will be beneficial. I would also, since you're taking out some meds with your water change, to add just a bit more back in with your dose. I know this seems drastic, but if he's had a few meds that haven't helped, then this may do the trick.
If you do decide to use Fungus Eliminator again, it says to do water change and a new dose on day 4 (I think -- I don't have that one in front of me.) I would do a water change on day 2 with a half dose of the med added back in. On day 4, I would do whatever water change they suggest (25%, I think) and add another full dose. On day 6, another half dose if necessary.
Bettas may not look good for awhile when they get finrot, but if you look closely you should be able to tell if it's healing. I call it a "healing edge" to the fin. It looks like a whitish piece of "skin" growing along the frayed edges, to begin to bind them together. The color of the fin may take awhile to come back to the way it used to be, and the length will take a few months, unfortunately, but it should be healed, or beginning to heal, in a week or so.
Some bettas are more prone to finrot than others, but if you keep the "stress level" down, he should be fine. The factors that stress a betta the most are cool or fluctuating temps, current or fast water movement, and bright light. Make sure the temperature isn't fluctuating now, check to see if the water is moving too fast for him, and keep the lights dimmed during treatment. I put a towel over about half of the tank if I need to treat. The towel covers half the top and goes a little down the sides of the tank to make a dim area for him.
Just a few more thoughts: Sometimes my bettas only got finrot on one fin.
One of my previous betta's dorsal fin rotted completely off, but all the other fins were fine. Also, make sure any carbon is removed from your filter during treatment. The carbon will just absorb the med and the betta won't get the correct treatment. Hope this helps!