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its an application of the universal gas law. pV=nRT. Since pressure is dropping so does temperature. sure, there may be some friction from the gas passing through, but it is greatly outweighed by the loss of heat energy due to the reduction in pressure.
open one of your tank valves in the garage tonight. after your wife is done yelling at you about all the noise, put your hand on the valve. cold or hot?
The postulation is if your isolator is closed and you open it "will it contribute to a free flow?"
Now assume your regs are correctly configured and you have been breathing your right post and the left is still at full pressure. You open the isolator. The left tank cools. But the left tank's gas and valve temp isn't relevant as you aren't breathing on it (and the person in the video wasn't either)
The temp of the gas in the right tank will minutely rise as the left tank discharges into it and its pressure rises. Ergo opening your isolator during a dive makes no difference on the likelihood of a primary reg free flow.