Why does this happen? Modern electronic circuits consume power when they switch states. When a flip-flop inside a chip goes from 1 to 0 (or 0 to 1) power is required to make that change happen. A flip-flop is made out of a number of transistors. The effect I am referring to actually happens at the transistor level.
A typical display processor hardware pipeline has millions of transistors performing different functions. From wide polyphase FIR filters for scaling to complex de-interlacing hardware (which also uses polyphase FIR filters).
While the interface to the display may only be 18, 24 or 30 bits wide, the image processing pipeline can easily be 64 or 128 bits wide within the processor chip. This can easily result in hundreds of billions of state transitions per second within the chip.
Using the iPad as an example:
2048 x 1536 pixels
24 bits per pixel (assumption)
60 frames per second refresh
= 4.5E9 potential transitions per second
I say "potential" because the number of transitions are a function of the images being displayed.
When displaying relatively static and, more importantly, relatively uniform content, the transistors don't need to switch as often. On the other hand, if the content has many transitions, lots of switching takes place. And power consumption (and therefore device heating) can increase dramatically.
One example of such patterns that I remember testing probably ten years ago was a pattern where even pixels are white and odd pixels are black. In other words, as many full pixel transitions as can be supported by the interface. I remember burning my finger when I touched the FPGA. This, BTW, was an accidental discovery while trying to debug a hardware problem that only occurred --you guessed it-- when images where noisy and busy.
Video is the perfect spoiler here. And, if the video is noisy and of bad quality it can be even worst. With video you can have almost random switching patterns covering most pixels on the display. I also remember that helicopter-in-flight footage (camera aimed at the ground below) seemed to be particularly nasty because every single pixel is moving and there's potential for vibration and noise that simply makes everything jiggle.
I'm not sure if the thermal problems being brought-up by new iPad owners have anything to do with this, but hearing one of these reports on TV brought back memories of burning my finger on an FPGA when I accidentally discovered this little known side-effect of resolution. From iPad 2 to 3 the screen got four times as many pixels. And so, there's a potential for four times greater power consumption (by the display subsystem) and four times greater thermal requirements. I'm not saying that this is what's going on. I just thought that HN readers might find this interesting.