I live in Phoenix, so heat can be a problem for 6 months out of the year. It is already well over 100 every day, and temps around 115 happen regularly.
There are many things that can help the situation.
1) Air condition - this is key. I keep my AC at 81 during the day - the fog tank is in a warmer part of the house than the AC, so it probably is around 85 at the tank. No, this isn't too warm.
2) I have a big tank (~70 gallons). If you have a big enough tank, thermal circulation can develop, so yes, it gets hot near the top, but the bottom is cooler. There is a pond in the tank - the water in the pond helps regulate the temperature, especially since most of the pond is 'shaded'.
3) Keep your tank well planted and really humid. Plants will keep the temperature down (evapotranspiration can even have a cooling effect - not much, but a little). Taller plants that create a canopy keep the ground cool. Other shade in the canopy stays even cooler - especially if you have a pond or other water feature near by. The higher humidity also helps regulate the temperature. Frequent 'rain' with cooler water can also go a long way to lowering the temperature a bit.
The thermostat in upper reaches of my tank regularly reaches 85 and has topped 90 before, however, I have never observed stress in my frogs in these cases. When it gets hot in the upper portions, they hang out in shade and by the water - where it is significantly cooler.
Remember, most of the species do live in areas where it gets hot. Have you ever been in the tropics/jungle in summer? It is very hot and very humid. Highs are in the 90s or even 100s and lows often don't get below 85. What I'm saying is these frogs are adapted to this. Don't let it get too hot, but when people say it can't get above 80 in a tank, they are being kinda rediculous. Just give the frogs what they need, high humidity, and micro-climate environments where there is water and shade that are cooler. Realistically, you need a bigger tank that is very well planted to achieve this.
Sorry for the length of this, but living in AZ has made think about heat and do lots of research.
To sum up:
1) AC - keep it cool, but you don't have to overboard
2) bigger tank is better
3) high humidity and lots of plants (create canopy)
4) pond or other water feature
5) make sure the tank is postioned in your home in a place where it doesn't get direct exposure from windows and such - even find the coolest place and move the tank there.
My wife and I both work all day, so these keep it cool without much direct attention and effort.
If these methods don't work for or are not realistic, the other advice that you see in this thread ought to help out.
Ken