I've just bought a new laptop that has an eSATA connection. I have a couple of 3.5" internal hard drives that I want to turn into external ones to use with the laptop. Now am I correct in assuming I wouldn't need any power supply to drive the drives as it would be done by the eSATA connection? Am I also correct in assuming I wouldn't need any cooling device for them as they'd be operating outside of the confines of a desktop PC?
Let's see. 1) putting your HDD in one of those will give you the same electrical characteristics as putting it in a cardboard box, or a Ziploc bag. That is not an external enclosure, it is a rubber baby buggy bumper.
All 3.5" drives used in external enclosures require a separate power supply. There have been couple of threads looking for counterexamples; none were found. The wattage consumed by a Caviar Green is more than twice the wattage that USB 2.0 can handle, and still twice that of USB 3.0. In addition, the drive requires 12V power, and USB provides 5V power. eSata does not provide power.
You may not need a cooling _device_, as in fan, but the case must supply some kind of radiative cooling or your drive will be poached, then fried, then incinerated. The drive generates heat, which must be dissipated (I spelled that incorrectly, didn't I). Most external enclosures do this passively.
OK. So you need an enclosure for an SATA drive that offers an eSATA connector plus a power supply. You can buy one per drive, or you can buy a handy-dandy dock and just plug whichever bare drive you want to use into it.