If it's not even getting warm to the touch within seconds of being turned on, I'm a bit doubtful it's thermal expansion/contraction of the plastic causing the noise.
I'm at a loss to think what could be the case though. My first thought would be a mechanical part, but that would happen almost instantly and then shouldn't cause any noises when you shut down.
Unless there is something "locking" into place when you shut down. And something "unlocking" when you turn it on. But if that were the case, it'd happen on all PS3 slims.
Perhaps it's something to do with the PS3 Slim BluRay drive lens mechanism. Maybe when you first turn it on and then when you turn it off, it's making some kind of movement (cleaning or diagnostic) that's causing that noise?
Regards,
SB