Me too Gman2.
Think of your stereo or tv. They are always in "stand-by" mode, that\'s how the remote works, and those devices never over heat(due to being in stby).
When in stby mode with most devices, the only thing that is getting power is a transformer. This x-former is outputing a small voltage(3-5vdc) to a couple of analog devices, maybe a relay and a switch/sensor. That way the device can detect a remote signal to turn on, such as in your stereo, or, the device can detect someone pushing the power/eject button on your PS2.
These devices getting the power in stby mode are "high-life" type devices which typically have a life of hundreds of thousands of hours before any possible failure. Now, there\'s always a small chance you could have a defective componet in that circut, but even those chances are minimal considering the simple nature of their function.
Don\'t sweat it, leave it in stby.