If it were me and it was a larger ssd 512GB or bigger, I would attach the drive to the computer from outside of the computer. I'd set the ssd on a surface that will not catch fire for example on a concrete type tile, then use the drive for a few weeks and see what happens. If the drive never gets hot or doesn't have any other problems, I might continue to use it.
If it was one of the smaller drives 120gb or 256gb I may do the same test above depending on my budget at the time, but would be far more likely to just replace it. The 840 evo's and evo pro's have come down in price quite a bit. A 256GB drive goes for around $134 on newegg. Sometimes cheaper, shop around, newegg, amazon, tigerdirect, microcenter, etc.
Now the more important question here is what caused the sata plug to melt in the first place. Is the connecter an adapter of some sort? Or was it a direct plug from the power supply? I would probably cut that end off and put electrical tape over the wires if it was a direct connection to the power supply. If it is an adapter, don't use it again. Ironically I have seen other sata power plugs melt but in all cases the hard drive that was connected is what caused the failure. I have seen a few molex plugs melt but those could be plugged in incorrectly if you really forced it, also this nearlly always burned out the drive plugged into the molex.
Edited by zingo156, 20 June 2014 - 10:28 AM.