There is no barrier at the boundary of different temperatures, the molecules can pass freely from one side to the other unless something else is holding them in place. What is important is how the movement of energy affects number of microstates on the either side as this tells how probable is such flow.
There is. The mixture of those joining molecules forms the barrier. Or else we gonna have salty river and blunt sea water. Neither transgress the other.
It's the same with Panama Canal. Ships from both sides can't just sail through without going through water "reconciliation" gates at that canal due to Atlantic and Pacific oceans "partitions" (density, salinity, temperature etc).
http://answi.blogspot.my/2017/08/why-dont-waters-of-atlantic-and-pacific.html