Why are you telling people to buy a 12V power supply for a 9V device and then saying it will run "cooler"? Is this thing selectable or did you post the wrong link or something?
A better supply than the original is not hard to find because everything is IC based now instead of transformer based. 9V 1000mA. If it's not a complete POS then this is all you'll need.
Even when using the original power supplies as mickcris stated will show a lower voltage when under load. So I went through the 4 PAD-129's and one PAD-130 I have sitting here and tested each one under load using a HuCard and then reading a game disc.
The lowest voltage I saw out of the 5 original supplies while reading a cd-rom game disc was 11.75v. The lowest voltage I saw with the 5 original power supplies while having a HuCard in the system was 12.25v
This tells me the 12v regulated supply will be about the same as an original supply rated at 9v.
So yes, I was wrong to say it would run cooler, but I was right to recommend a quality regulated 12v supply.
The 9v supplies I have and tested work in these systems just fine with original cd-rom game discs. As soon as I try a burned game these 9v supplies no longer allow the system to read discs. Simply swapping the 9v supply out for an original or one of these 12v supplies allows the burned discs to be read. I have not found any exceptions to my testing.
The 9v supplies are good as long as you don't want to use burned discs.