the external drive would get hot if it is heavily used i guess .. but that is normal for harddrives .. they spin at many rpm
have you considered the possibility of your BIOS not recognizing the USB HDD . therefore not booting from it.
Use Plop boot manager to boot from your USB hard drive.
@ bkmfs don't hijack threads . he is not using 3.0usb so the answers might be mixed . Open your thread for this .