So far from my experience it only boots up if it wasn't used for really long hours, and it entirely cooled down. If I turn it on, and turn it off a little later, try to turn it on again, it is only worse and worse every time. For example, if it isn't turned on for a day it boots up, if I turn it on again it boots, but there are texture / pixel errors, if I try to turn it on again only black screen, and nothing else, it doesn't even recognize the controller/etc....
I think probably a part of the RSX got damaged somewhere, and the console only boots up properly when it's entirely cold, maybe some part expands due to the heat, and that's why it becomes worse when it gets exposed to heat.
While replacing the cooler may help a little, I think sadly it won't fix this problem, as the console shouldn't get this hot so fast. If I find out what is the exact problem I'll post about it.