My Lenovo laptop has an eSATAp socket but no USB3. Speed not far short of USB3. the "p" is for power, there was an eSATA socket.

I bought an eSATAp external disk disk, (2.5 inch) and that does not over-heat. Since then I bought an eSATAp case and fitted a 2Tb 2.5 inch disk. Both perform well, and they both have a 5V socket which you could power from a mains power pack. Both externals have USB3 sockets too.

Have you considered using the RJ45 Ethernet port (Or even a WiFi version) for external storage?

Ports on the E73:

    Front ports
    - Two USB 2.0, microphone (stereo, 3.5mm), headphone (stereo, 3.5mm)
    Rear ports
    - Two USB 3.0
    - Two USB 2.0, serial (9-pin), optional 2nd serial (9-pin)
    - Optional parallel (9-pin), keyboard (PS/2), mouse (PS/2)
    - Ethernet (RJ-45)
    One Intergrated VGA port
    One Integrated Display port
    PCIe WLAN4 : 11b/g/n wireless, PCIe Half Mini Card, Intel Centrino® Wireless-N 2230, Wi-Fi + Bluetooth combo adapter, 2x2 (selected models)
    Ethernet : Gigabit ethernet port, Realtek RTL8111GN, Wake on LAN®