Portable thermal camera readers are often used to determine if there is, or what device, are hot in the board. If you get an affordable one, perhaps you could be able to - with certain degree of accuracy - determine at which region of the chip the heating starts and then have a clue of the candidates outputs that are sinking overcurrent. If you have luck, you could even determine what other devices/tracks on the board others than the microcontroller itself are hot aswell.