I'd like to do a blind test on power cords, too. Power goes all over the county on high voltage lines, step it down at ana xformer, goes through the house in 12-14 AWG ROMEX, through a gazillion dollar power cord that magically realigns the power (how it ever "knows" what it "was" when it left the plant I'll never know) and THEN goes into a CRAPPY IEC outlet, and THEN into the simple wires from the IEC outlet inside the amp to the power DC supply circuit block. Any decent DC block will turn all the AC to pure ripple free DC. If it doesn't, no power cord is going to change that.
Since this comes from the OP, I will assume its fair game.
The reason power cords make a difference despite the limitations described in this statement has to do with voltage drop in the power cord. It also has to do with how DC power supplies work.
These effects can be quite measurable!! For example, I have seen a 3 volt drop across a 6 foot power cord cost a tube amp of about 35% of its total output power. If you want a reason to look for, that one is pretty basic!
But there is more. Most DC power supplies have a power transformer, a set of rectifiers and a bank of filter capacitors. The circuit draws its power from the filter caps, which are replenished by the transformer and rectifiers. Now its a simple fact that the filter caps are not seriously drained in between cycles, else the amplifier will not work very well. But the rectifiers will only turn on at a certain time- whenever the voltage from the transformers is higher than that of the filter caps.
This only happens at the peaks of the incoming AC power. IOW, the power supply is only doing its work in very short bursts of energy. Now in normal operation what this means is that the diodes are doing some fairly high frequency service; they may only be on for a few milliseconds per cycle. This is called commutation- the turning on and off of the rectifiers, and the current that might occur at these times can be quite prodigious depending on the circuitry of the audio device.
Meanwhile the power cord may be doing double duty, especially if the amplifier has a filament circuit.
Consequently you have two effects: voltage drop at 60Hz, and the current ability at a fairly high frequency. The greater the demand on the cord the greater the likelihood that its effects will be audible on this basis; OTOH the lower the current and the more regulation employed by the audio device the less audible it might be.
The bottom line though is you do not have to look any further then these two phenomena to find something that is not only measurable but also audible and independent of anything upstream of the cord.
With regards to warmup, I remember a Sanyo amp from the mid 1980s that had a passive freon heatsink. It sounded best cold (MOSFET output section)- as soon as it warmed up, the bass was gone. A fan on the heatsink really helped but it was at its best if you kept the amp outside during the winter. I do most of my work with tubes though, and these days it seems that if the amp/preamp needs more than about 2 hours to get to where its going to, it may well need new filter caps or the like. We have measured voltage differences between power supplies that are not broken in as opposed to those that are. This seems to have mostly to do with the filter caps forming up. While most of that happens fairly quickly, a cap might take a few weeks to really reach full efficiency, depending on how much use it gets during that time. The explanation we got from an engineer at Cornell Dublier was that there is a certain amount of water molecules that has to be chased out of the electrolyte by the operation of the cap. Sometimes that can take a while.