Moving an eSATA drive from a Firewire enclosure to a Thunderbolt enclosure

I want to move an eSATA drive from an external Firewire enclosure to a –yet to be purchased– Thunderbolt enclosure and connect it as the same volume. I think it should be possible since it's the same internal interface, but then again, I want to check and confirm that there won't be any surprises. Are there any specifics for a Thunderbolt enclosure that I'd need to pay attention to, or would I generally be better advised to get one of those Thunderbolt to Firewire adaptors ?