Chip overheats insantly, could it be a result of having burned it while soldering?
You didn't destroy it from soldering. First, it's almost impossible to destroy the chip from soldering heat for a short period of time, and typically you'll wreck the board long before the chip breaks a sweat. 

However, it's surely fried. There are a few possibilities as to how it could have gotten that way. Reversing the supply, even for an instant, will do it. Applying a signal to an input before power is applied to the chip, then applying power can do it (or the classic equivalent when a test prod slips and shorts some random connections together). The Arduino may be able to supply enough current to cause that to happen.