Although it can be done, I'm not certain why you would set lash that way with either solid or hydraulic lifters. As far as temperature, there's not going to be a significant change in the valve train as you go from #1 to #6. It just doesn't cool off that fast that it makes much difference. Besides, you can always warm it up and check again from the other direction.
It's easy enough with a solid lifter to set the lash, cold or hot. If you do it with the engine running, you may not get consistent results. All you could hope to accomplish would be to insert the feeler gauge and listen for the ticking to go away. But at that point you wouldn't know for sure if it was just right, too tight, or still a tad too loose. Too loose and you lose lift, too tight and the valve isn't going to seal and transfer heat properly. The result could be lost power or burnt valves.
You actually only have to rotate an inline six crank two revolutions to get all the valves in a position to be adjusted. Start with #1 at TDC and adjust #1 intake - #1 exhaust - #2 intake - #3 exhaust - #4 intake - #5 exhaust. Then turn the crank until #6 cylinder is at TDC, and adjust #2 exhaust - #3 intake - #4 exhaust - #5 intake - #6 intake - #6 exhaust.
With hydraulics you have a preload range, usually up to .100" and sometimes more. With them you simply tighten the adjuster to zero lash then add another 1/2 to 3/4 turn to add some preload to the lifter. If your adjuster is a 3/8-24 thread, then you know exactly how much preload you put on. For example, 3/4 turn is exactly .03125" of preload. (BTW, this is not the case for stud mounted rockers. That math is slightly different).
Just turning until they get quiet with the engine running, might get you inconsistent results.