African Dwarf Frog (Hymenochirus) which is a tropical species, should tolerate 81F. However this is probably still a bit on the warm side, but I believe on the upside of tolerable for this species. Lowering the water temperature slightly may be more ideal (77F).
1. Get a bigger tank!! Why? Larger volumes of water are more stable and less prone temperature (and overall chemistry) changes. A 3 gallon tank is simply going to shift to ambient room temperature VERY quickly vs 30 gallons of water. Even a 10 gallon tank (Walmart $12 dollars) will hold temperatures a lot better than 3 gallons.
2. Place a box fan (or similar fan) next to the tank, circulating air over the tank may drop the temperature a few degrees.
3. Use a screen lid rather than a glass lid, more evaporation means cooler temperatures, but you'll need to replace the evaporated water.
4. Do daily water changes with cooler water (this would work better with a larger aquarium).
5. If temperatures really get out of control, use a ziplock bag of ice to bring the temperatures down (I had to do this last year with my african clawed frogs when my central A/C unit broke down and outside temps were 100F+ all summer).
That's all I can think of for cheap methods.