Are you talking about the LEDs that drive the backlight, or are you talking about the actual LCD that produces the colours?
Assuming it's the brightness you're referring to (the LEDs), it's probably be related to the system's inbuilt power transformer (which'd definitely warm up a bit with half an hour's use). It may even just be that you've got a disc in the drive, and that's how long it takes before the system decides to spin it down and stop sending it power.
Regardless, I wouldn't be too concerned. After all, the only real precaution you can take is to back up. You should be backing up anything important to you whether you think there's an impending problem or not - the whole point of doing it is to do it while you can. There's not much you can do to stop a system failing, but you can at least be prepared for if it does!