I'm not sure about the energy ratings on my refrigerator, but it is a fairly recent model (about 3-4 years old) and is certainly not an energy hog. In my opinion, the benefit of power cord burn in on a fridge has nothing to do with the continuous draw and everything to do with the heavy surge when the compressor kicks in, even if it is rarely kicking in. My experience is that even supposedly fully broken in cords (ie. cords that have been in use on my integrated amp for 6 months to a year) showed noticeable improvement following a week on the fridge. The adapter necessary for this, by the way, can be bought at many electronics parts stores for about $3.
My amp is not a monster (about 70W per side), so your experience may vary if you have very high powered amps, but other than that, any other piece of equipment will never ultimately and fully burn in a cord the way a fridge or chest freezer does, including computer monitors/towers, large box fans, etc. Haven't used any larger heaters here though. That is my experience.
