Well, someone please feel free to correct me if I am wrong, but here are my thoughts:
I can't imagine that the heat loss would be incredibly significant. Myself, I have the tank set to 78 degrees, and my ambient room temperature is usually about 70. It is true that the water sitting on the floor in a bucket or container will begin to cool, but with 8 degrees difference, it won't be excessively fast. Also, you have a steady drip of water coming into the bucket water at 78 degrees, which should also slow cooling. I can't imagine any more than a few degrees difference, even after an hour or 2...
Tecwzrd's idea sounds good, but if you are worried about the heater, how about this? After drip acclimation, you could quickly scoop the fish or invert into a bag, and then float that on your water for another 10 or 20 minutes...then not only will the majority of the water in the bag be from your tank and the fish or invert properly acclimated, the temperature would be perfect too...then you could scoop them out of the bag and put directly in your tank?
38 Gallon (Freshwater): 1 Green Swordtail, 3 Yo-Yo Loaches, 1 Clown Pleco, 1 Blue Gourami, 4 Otocinclus, 7 Cherry Barbs.
46 Gallon (Saltwater): 60 pounds Lalo Live Rock, 60 pounds aragonite sand, 1 Coral Beauty Angelfish, 1 Peppermint Shrimp, 1 Mushroom Coral, 1 Emerald Crab, various snails and hermit crabs.
10 Gallon (Saltwater quarantine):