When using an external power source to the arduino, measure the voltage between the arduino +5v pin and ground. My arduino/ethernet shield combo was outputting 8v+ when connected to an external 12v power supply.
Now that is odd.. It sounds like the regulator is being overloaded/heat-failing if it's jumping that high, to say nothing of dangerous to anything connected to the +5V bus.(of being burned-out by running +3V over.)
I've had the same problem of the 5V regulator getting hot, and sometimes having the whole ethernet board stop working because of it.. I thought the board had it's own regulator? checking schematic... Yep, It's a 3.3V regulator, that appears to be drawing off the +5V bus for +VDD. Which would explain the draw on the arduino's regulator.. the MC33269D-3.3 is supposed to have a maximum input voltage of 20V, which doesn't make sense why it's not drawing from the Vin (unless, as someone pointed out, and I accidentally shorted Vin to GND on a breadboard, the trace on the Arduino is not able to handle the draw.)
I've even had the 5V regulator run warm, even with just a 7.2V input. (i'm trying to make a robot, with power from a 7.2V RC car batteries.), and usually that's the low-end for the 5V's input. (which is still plenty for the ethernet router, which originally had a +9V, 1-Amp wall-wart, but it too, is only feeding to a 7805 regulator inside.)