MarkT:
The leads you solder too are not directly connected to the silicon chip, there are tiny thin gold wires
that do that, and it takes some time for heat to flow along them and overheat the silicon. Keep soldering time to a couple of
seconds per joint and you will be fine.
It's also a good idea not to solder adjacent pins in succession. Alternate between opposite sides of the chip so it has less chance of creating hotspots. You can also do all the even-number pins followed by all the odd-number pins if you want to.... 