I highly doubt it was the soldering iron that killed that diode. I've applied lots of heat during soldering and it has not affected the diode. Most of it dissipates into the case, and rarely is there enough to actually cause the little wires in the diode to fry.
More than likely the laser is LEDed (dead) because: 1) the current was not set properly to a known value using a dummy load, and 2) the lack of a heatsink so that when you turned it on, the heat generated by the power going into the laser was not dissipated properly. If #1 didn't kill it immediately, then #2 probably would have in short order. The laser diode may also have been fried from the driver not being properly shorted out before soldering.
Next time--and before spending money on another diode--you should buy a multimeter and a heatsink for your build. Then construct a dummy load and attach it to your driver, and measure the current that will be sent to the diode using the dummy load so that it is at the expected value. Then desolder the dummy load and short the leads of the driver to clear out and residual charge, and solder the driver to the laser diode you pressed into your heatsink.