Unfortunately we'll always need the pipe to blow air outside. The heat has to go somewhere. Even with this invention, if they're converting heat to electricity, they will have to release at least as much heat as they converted to electricity.
Indeed, this can be demonstrated by running current through a plain old Peltier cooler without a big chunky heat sink attached. At first the cooler will have one side heat up and the other side get quite cold, but within a few minutes the entire block becomes evenly warm.
Eh, doesn't all modern air conditioner just do heat exchanging? no need to actually blow the air out - but yes you still need a pipe for the heat exchanging medium
