How can I repair an arduino Mega 2560 Rev 3 that has a short circuit?

My original Mega Arduino made a short circuit by connecting it to a sparkfun shield monster moto, now every time I connect it the RX, TX, ON and port 13 LEDs stay on and the microcontroller overheats.
My Doubt is
Is it possible to repair it by desoldering the microcontroller and exchanging it for a new one using a heat gun like the ones used for SMD components?

Sure, someone experienced in SMT stuff would be able to replace the processor, assuming you also have the right tools.

It would probably be cheaper to order a new ATmega2560 board from China though.

Also bear in mind, there may be other components on the board damadged also, so you might replace the processor and the board will still not work.

I have the tools, and have soldered up ATmega2560s, but if it was my board with those symptoms, I would bin it.

Schwarze_herz:
now every time I connect it the RX, TX, ON and port 13 LEDs stay on and the microcontroller overheats.

Well, here's a problem!

If it is a real Mega, then the Rx and TX LEDs are driven by the USB interface chip, an 8U2 or 16U2 chip, not the 2560. But the pin 13 LED is on the 2560 (and the comparator). So whatever you managed to do, it suggests all chips are fried.