The Thermaltake BlacX connects to one of your USB 2.0 ports and does not connect to a SATA port, so you do not need a ESATA port to connect to. You can hot swap a 2.5" or 3.5" SATA drive. The Thernaltake BlacX Duet has both an ESATA and a USB 2.0 port and accepts two drives. If you want to use ESATA you will have to purchase the bracket NoCheese indicated if you have a free internal SATA port.
First, make sure you recognize the distinction between the interface between the external case and the drive(s) it contains - in this situation, the case accepts a SATA drive (not eSATA - there is not eSATA HDD) - and the interface between the case and the host computer, which could be USB2, eSATA, Firewire, etc.
Thermaltake's website shows they make four products under the BlacX name. All have a USB2 interface to the computer; two (including the Duet) have an additional eSATA interface choice. The USB2 will work, but eSATA offers the potential of faster speeds. A true eSATA port on your mobo also allows other things like hot swapping, which the Thermaltake unit supports. If you get one of the adapters others mentioned, you MIGHT get that. This is because the adapter is merely a connector changer with no processing, so it depends entirely on the capabilities of the regular SATA controller in your mobo. Many makers included some eSATA features, like hot swapping and long data cable lengths, in their regular SATA controllers, but some did not. If you don't need those extended eSATA features, it doe not amtter at all - the adapter will do what you need well. But if you NEED hot swapping, for example, check details carefully with your mobo maker.