Unplug your power supply and check the voltage of your power supply going into the Arduino, unplugged.If you use an external supply, it needs to be within spec. Max is typically 24 vdc.If you are using usb cable, it too needs to be within spec, and this is 5 volts dc.
check the voltage of the Vin pin, it should be the same reading as you read before.Next, check the output voltage of your onboard regulator, you should read 5 volts all being well.If it is significantly greater than 5 volts dc, remove power supply and replace regulator.If voltage is 5 volts dc, and board is cool, and you removed some wires for I/O, then suspect your I/O or the way you are using your I/O ports, check software.Try loading a simple blink program, dos it still get hot?
You potentially have an issue with the electronics on the Arduino.
The same thing happens if we use a dc power source on our test bench, using this source the arduino does not heat up no matter how much current we're drawing, but if we use batteries then the arduino starts to get very hot to the touch.