I agree with Debbi, Rams shouldn't be stressed at all with temps around 85, and that won't cause ratty fins. Either way, if its 80 degrees in the room, just remove the heater so it doesn't make things worse in the mean time. Put the new one in when you can.
Is it possible your ammonia kit is faulty/old? It is worth the piece of mind to create a control sample maybe? Add 3ml of household ammonia to liter of water (doesn't have to be exact) and test it with your kit to find out if it is properly recording positive results. Sometimes- especially if its been through a warm spell the reagents can degrade and become ineffective.
In a densely planted tank that you obviously take good care of the odds are against an ammonia spike, but I can't help but think the rapid breathing, the stress and the ratty fins all point to ammonia burns. What if you experienced a die off in the bacteria in your filter when it shut off? Could it take 48 hours+ for an ammonia spike to become evident? Your filter would still process some, and your plants will take some up, it could have taken a couple days to reach critical levels and with a filter that was still colonized the bacteria could have grown back relatively quickly? Perhaps your ammonia was only elevated for 2-3 days before things settled down and got back on track and what you are seeing now is just residual effects from some burns the fish might have experienced? With only one or two of your more delicate fish showing these symptoms and the filter malfunction I have to think that a slight temporary increase in ammonia is the most likely cause.
I don't know that there is more you can do than you've already been doing. Add an airstone (if you have one) to saturate the water with 02. The fish are breathing heavy, this will make it easier on them. Also, I would avoid the ice bottles. Rams really are fine in the low to mid 80s. I keep my rams at 82 all the time. The coreys may not like it too much, but the rams will be okay. The reason I think you should keep the temps warm is because ich can't attach to fish at 82+ and if the fish are already stressed you're more likely to experience an outbreak at lower temps. Better safe than sorry. Just like a heater that won't keep a constant temp, you'll find the same thing with frozen water bottles. If you have a real heatwave and it gets into the 90s, then you may have to take some action, but for mid 80s, don't mess with it.
Is it possible your ammonia kit is faulty/old? It is worth the piece of mind to create a control sample maybe? Add 3ml of household ammonia to liter of water (doesn't have to be exact) and test it with your kit to find out if it is properly recording positive results. Sometimes- especially if its been through a warm spell the reagents can degrade and become ineffective.
In a densely planted tank that you obviously take good care of the odds are against an ammonia spike, but I can't help but think the rapid breathing, the stress and the ratty fins all point to ammonia burns. What if you experienced a die off in the bacteria in your filter when it shut off? Could it take 48 hours+ for an ammonia spike to become evident? Your filter would still process some, and your plants will take some up, it could have taken a couple days to reach critical levels and with a filter that was still colonized the bacteria could have grown back relatively quickly? Perhaps your ammonia was only elevated for 2-3 days before things settled down and got back on track and what you are seeing now is just residual effects from some burns the fish might have experienced? With only one or two of your more delicate fish showing these symptoms and the filter malfunction I have to think that a slight temporary increase in ammonia is the most likely cause.
I don't know that there is more you can do than you've already been doing. Add an airstone (if you have one) to saturate the water with 02. The fish are breathing heavy, this will make it easier on them. Also, I would avoid the ice bottles. Rams really are fine in the low to mid 80s. I keep my rams at 82 all the time. The coreys may not like it too much, but the rams will be okay. The reason I think you should keep the temps warm is because ich can't attach to fish at 82+ and if the fish are already stressed you're more likely to experience an outbreak at lower temps. Better safe than sorry. Just like a heater that won't keep a constant temp, you'll find the same thing with frozen water bottles. If you have a real heatwave and it gets into the 90s, then you may have to take some action, but for mid 80s, don't mess with it.