I've actually had too many problems with dripping-and I'm guessing maybe they're caused by the temp thing? Now, if I acclimate anything, I just float a specimen container in the tank, with just enough bag water to cover the coral/fish/invert, then start adding water from the tank with a turkey baster until the container is full. I'll take upwards of a few hours to do it, just whenever I walk by the tank, squirt some more in. If it's a coral, add some CoralRX or Revive right before I put in the tank, then discard all the mixed water. So far it's worked pretty good.
This is exactly how I do it, too. Too many times, using a standard drip method, I noticed that the water in the bucket was getting too cold. Doesn't help that I have a ceiling fan in the same room as my tank.
Another possibility might be a pH difference. Inverts are very sensitive to pH differences. Even when dripping, if the water, in the bucket, isn't "in motion," or getting enough aeration, the pH could be dropping quickly.