See, the whole idea is that science should use precise terms whenever possible.
Add this to the fact that each listen is not exactly reproducible, you need to have a control sample to say that "so and so happened due to burn in".
Otherwise you might be seeing the effect of:
A) expectation bias
B) listening more closely
C) humidity difference
D) temperature difference
E) different placement on head

All except A can be averted by using a control pair of headphones/amplifier.
(I do not negate the effect itself - there's enough mechanical stuff in headphones that can be affected - at least pads and headband, perhaps cups - esp. wooden, usually not the driver, except if it's really lousy material. Amps... nada, unless by burnin you mean lousy electrolytic cap burnout.)

Also: slightly more extended -> x Hz more extended OR y dB/oct less rolloff
warmer -> x dB boosted at y Hz OR more even order distorion OR less odd order distortion OR less high frequency ringing at z Hz
has more slam -> is it more subbass or what? see "more extended"
lowered noise floor -> from what dB to what dB?

Certain cooled parts do indeed change their characteristics enough. But this is typically out of their spec, so there you go.