Place it in a zip-lock type bag and remove as much air as you can. Place it in the freezzer for several hours or longer. Remove the drive and wrap in a towel or something to insulate it for a bit. Connect and try.
You may need to do this for longer periods.
This does not always work but it has worked for me a number of times. One recovery had the drive on the freezer for several days.
If the electonics on the Buffalo case are damaged, you may need to open the case and freeze just the drive. Then connect with some sort of adapter(USB-SATA, etc)
While some may say freezing causes more issues, many are recovery companies/employees. All I can say is that it has worked many times and that there was no intention of using professional recovery. Risk was low for me.
After that, it may be necessary to have a professional recovery done. That can cost to the thousands of US dollars. Note that some will not charge if no recovery