The correct answer is "it depends" on what everything is made of. ALuminum heads for instance expand and contract at different rates than cast iron. Also, I disagree that "it changes very little" and here's why I disagree. I've had a LOT of engines through the years with solid lifters. They always and I mean ALWAYS get quieter when they warm up. That is.......with cast iron heads. I have very little experience with aluminum heads as I've never had the coin for such.
"It depends" is the standard engineering answer. The valves get the hottest, and they expand the most, which reduces lash. The pushrods get hot and this also reduces lash, but not as much. Remember, the growth is a certain amount
per inch so longer parts grow more, assuming uniform temperature.
The block and heads get hot and that
increases lash because it pushes the rocker arm further from the 'center' of the motor. Aluminum heads will expand more. So the net is some 'cancellation' of the decreased lash from valve growth.
For example, if it's an Evolution or later Harley, the expansion of the aluminum cylinder and head increases more than the pushrods and steel cylinder studs, so if you don't warm up your Harley, you'll pop head gaskets and base gaskets when you beat on it cold. This also means that on the aforementioned Harleys (which are all pushrod), the lash
increases as it warms up since the pushrods are steel. This is mitigated somewhat by the tension of the cylinder studs, but lash does increase and setting the cold lash on HD's is just adjusting so that it has no lash but still free-spins, and it loosens slightly from there.
Overhead cam engines mitigate most of this and then it's just down to head material, valves, and whatever's between the cam and valve. Most jap bikes just have a bucket and shim, and the clearance hot becomes very small. As long as it's not negative lash, you're fine.
All my motorcycles and other adjustable vehicles get done cold. But I adjust my slant wet and I hate it. I adjust to specs and then tweak each valve just a tad by ear. You end up with the valvetrain quiet and smooth as possible.
And I love it when guys go "Motor's quiet, no need to adjust the valves!"
That makes no account for the valves being
held open and burning since they cool through the seats! Be careful trying to make it quiet!