Ps3 Power issue, how do I fix this?

But, how could it be overheating if it does it as soon as I turn the system on, without it being on at all throughout the day prior? Is there any way I can just prevent the YLOD without having to repair it that way?

If the compound is starting to get hard, it will "shrink" a bit when cool. That means that the first time the PS3 is turned on, the unit will overheat because the compound is essentially not working (has gaps). With the CPU heating up, the compound may be making better contact which is what is needed for it to work properly. Thus... it works!! Until the unit cools down again and the process starts all over again.

note: this is just a guess that explains the reported behavior and does not mean that this is the actual problem.

That... actually sounds like it's most probable. My room is always around 50-60 degrees fahrenheit, it gets cold in here, and it does take a while until the system does power on fully. Enough time for it to have warmed up regularly from powering on and off again repeatedly, and it (from what it seems) has been taking even longer to turn on if I quit trying for a while and let it cool down a bit. It also stays on gradually longer (though only by a second or two) the more I try until booting it up. After a few tries being just long enough for me to hear it boot up and see the screen actually appear on my tv just before it turns off again, and rinse and repeat a few more times when it finally stays on. So if that is the case, how do I fix that, just keep it in a sort of warmer spot? Or keep a small heater near it or something weird like that to warm it up before I try powering it on excessively?

The"fix" for this, if I am right about the compound, is to replace it with new. Open up the unit and take off the old compound and replace it. There are dis-assembly videos available to guide you through the process.

Can I just leave my system on but idle so I don't have to replace anything? I don't really want to pour more money into it. As I said, my room is really cold, especially at night, so I don't think it will really overheat if it's only idle and on. My Uncle never ever turned his system off and it was just fine. Maybe I can try that for a while before already replacing things when I just received the unit less than two weeks ago.