What did you do that could cause this ?
It is quite rare for them just to get hot for no reason and stop working.
Schematic of what you have/had connected would be a good place to start ?
Actions you were performing when it went to its current state ?
Also please read the posts at the top of this forum section as there is some exceptionally useful information in those as to what and how we would need to see in regards information.
The hardware on the board has been damaged. Whatever part is getting hot, plus probably other parts. It is likely that one of the damaged parts includes the serial adapter IC - this is a surface mount part that can't realistically be replaced at home unless you have hot-air rework tools and the experience necessary to use them.
Most likely the power rails were abused in some way; official boards (and clones using a 16u2) are particularly susceptible to damage in this way. Applying an external voltage to the 5v rail while the USB port is plugged will often damage it like this.
DrAzzy:
Applying an external voltage to the 5v rail while the USB port is plugged will often damage it like this.
That sounds like what I did. A shield that I was using was also supplying power to the board. Thanks for your help.
I will check if an external serial adapter can still communicate with the board—otherwise I'll remove the AtMega and maybe try to salvage some other parts …