It depends on what model you have; mine is one with full PS2 backward compatibility, and it burns with the heat of a thousand suns, or 10 first to third model xbox360s, your pick (seriously, my ps3 runs hotter than my 360) A friend of mine has one with the partial PS2 compatibility and her's runs just as hot, but multiple other people I know who don't have a ps2 compatible model, theirs runs nice and cool.

If yours is a PS2 compatible model, standing it vertical is probably better... most of the heat tends to come from the right half of the machine, so standing it upright will allow it to escape just a bit easier. Consider using compressed air to blow out all the dust through the vents (front to back is usually the best exist route), because the more dust that builds up on the heat sink fins, the harder it is to dissipate that heat. I don't know how well canned ait will work, I used high-pressure condensed air from my job... it's piped all around the factory, and it's so powerful it will actually break your skin if you spray it on yourself

As far as the noise, the fans never slow down because the machine stays at or above the trigger temperature once they engage. The machine only cools down after it's shut off... and that's dangerous too because the fins are still hot, and then all the heat is left stationary inside the console. Your fan noise could also be a sign that your machine badly needs to be dedusted, because I've never once heard my machine's fans despite feeling some heavy heat out of the back... but I also only play Wipeout HD, and I haven't been playing it at all in ambient room temperature above 75 degrees...

Consider an intercooler; they only got a bad rep because the first model for xbox was poorly designed and actually drew its power from the OPERATING power lines of the 360 instead of having its own power source. I have two different models, one that clips onto the right half of the machine and triggers when it senses too much heat, and another that hugs the back AND right side, and plugs in-line the 120v power plug (thus not actually affecting the machine itself). Both designs can get a little noisy, but I'd rather have some noise than a molten pile of metal and plastic.