I think the recommendation to check compression at operating temperature dates back quite a long way, and it has to do with getting better and more consistent readings once all the parts have expanded and you have normal operating clearances. It's probably less necessary on modern engines that were machined and built to tighter clearances and tolerances.
I found the best method is the same as what FlaHeatWave mentioned. Leave the ignition turned off so you won't get ACR's operating or fuel and spark, and jumper from the positive battery cable stud on the starter to the solenoid connection. I took an old cheap remote starter switch from my pile of old automotive tools and modified it slightly by installing a spade connector on one lead that fits the solenoid, and left the regular clamp on the other lead. Remove the plugs, block the throttle wide open, connect the remote starter switch, install the compression gauge to the cylinder to be tested, and then push the button and let the engine crank over until the gauge stops increasing. Write down the reading and then repeat for the other cylinder. And one of the most important things is the difference from one cylinder to the other. Ideally they should be very close if not identical, but in the real world on an engine with some miles on it that isn't likely. If you get a significant difference from one cylinder to the other, you need to do some additional testing, starting with a leak-down test.
Jerry