To clarify, your rig will only take longer to reach a stable temperature, if you use lots of water in that bucket. That water acts as a heat transmitter from your computer, to the fridge's cold coils, but that water is also going to be a buffer, i.e. it is going to delay the heat transition, if you use lots of it.
So the surprise is having to wait 6 hours to find out your REAL min and max temps.
I'm (strangely?) stuck with the idea that you're going to stick that bucket inside what's left of that fridge. If not, then the igloo cooler idea would work. It reminds me of the guy with the freon cooler... he used an igloo cooler, coated the insides, and used that to hold CO2 and Fluorinert.
http://www.octools.com/index.cgi?cal...ubmersion.html