I can't comment on growing 'cool' orchids, but I do know a little about heat transfer.
Based on the pictures at the Orchid Gallery website, this looks just like a regular terra cotta pot (but made with fancy white clay). The only possible cooling will be from evaporation at the pots surface. To keep moisture at the surface of the pot, I imagine you'd need a pretty wet mix inside the pot. How will the orchids feel about that? You guys know better than me
Of course if the surface of the pot is dry, there won't be any evaporative cooling, and the pot (and roots) will be the same temperature as the rest of the room. If you have a very humid environment then evaporation (and cooling) will naturally be less.
The thermal imaging picture on the
website definitely seems like a gimmick to me. They show two clay pots, with the 'cool' pot registering ten degrees cooler. Something is fishy here. Is the standard clay pot glazed? (keeping the surface dry) Is the standard pot completely dry inside? (and therefore no evaporative cooling). Did the 'cool' pot just come out of the refrigerator? I'm very suspicious.
The link provided by RosieC (to Ray's idea) looks like a great idea to me. And a small fan blowing on the pot would increase evaporation (and cooling) even more.