Recently, when I was doing a project with a breadboard, my Arduino started to get really hot. Like, 1st degree burn type hot. I unplugged my USB plug, and tried to cool it off. I think it was caused by improper wiring.
However, now, even if my Arduino is off of the board, it still gets really how when I plug it in. How can I fix this? No component really seems to be damaged.
High heat often indicates a blown processor; the IO protection diodes fail as shorts, connecting VCC and GND internally and really heating up when power is applied. Unless you have access to hot air removal tools to replace the 328P, perhaps the FT232 (not as likely), or the voltage regulator (not likely if you've been powering from USB), that Nano is likely shot.
Don't despair.
Everyone does it sooner or later and it only takes a millisecond to blow it.
If the whole chip is very hot, imagine what the delicate bits in the middle (the die) must be like.
If it is the processor, you can replace it, but whether it's worth it, I'm not so sure.
However, if you like a soldering challenge, it can be done.