I'm seeing a different heat issue with the PoE board.
If I run the arduino over PoE - then the three legged chip next to the DC power in port gets hot - on the uno itself - not the PoE board. And I mean almost burnt my fingers hot.
If I run the board using a non PoE port on my switch and use USB power then it does not get hot.
The sketch (temperature sensing with 2x DS18B20 sensors) runs just fine in both cases.
I have no idea why using PoE makes the chips on the uno (rev 3) cook.