So here is my personal opinion. Yes, having a filter and heater out for a whole day could have put a lot of stress on your fish especially depending on how heavy your stocking was.
I would NOT break down your tank. I would do a really good clean. Old but well rinsed tooth brush on any obviously dirty ornaments (take them out, clean, put them back), spot clean the glass, a thorough gravel vacuum, and a big WC. Since your fish are not exhibiting any current symptoms put the temperature back down to their optimum temperature. Continue to monitor them and take daily water reading if possible to make sure conditions are good for healing.
Here is why I suggest this:
-When you do a big WC it removes a lot of the bacteria/virus/parasite that might be living in the water and prevents reinfection of your fish (it can't infect the fish if it's not in the water!) giving the fish a better chance at fighting the infection
-Some parasites/bacteria live part of their life cycles dormant in the sediment of the gravel. A large vacuum will remove a lot of them.
-Breaking down a tank and temporarily housing your fish can stress them, causing there immune system to be depressed and leaving them vulnerable to another episode of whatever it was that attacked your tank the first time
-As with any animal, good living conditions allows the body to function optimally and be best able to combat disease on it's own. That is why regular WC, gravel vacuuming, and water testing are so stressed by many of the members on this forum. (as well as good food!)
-Medication has a time and a place. But, medications also have side effects and many put stresses on fish. If you are using the wrong medication you may actually be making your fish WORSE than if you just helped your fish combat the disease on it's own through optimal tank conditions.
What would I like to know more about to help you better ->
Give me the run down on your tank.
-What size is it?
-What are the current occupants?
-What were the original occupants?
-What is your WC schedule (be honest, no one should be here to judge- but to help)
-What do you use to test your water? (strips, liquid, the LFS)
-What kind of filter do you have?
-When you replaced your filter did you use the old media to seed the new? or did you just use the new?
I know a couple of these questions have already been answered, but it's nice to see all the info in one place, also testing water daily after getting a new filter is never a bad thing, just to make sure you don't go through a new cycle/mini-cycle which can take a while to show up.
Hope this helps and your fish make a full recover!
Also, remember that there is more to your water chemistry than just ammonia, nitrite, and nitrate. Who knows what other waste product your fish might be sensitive to!