This question remains unanswered until someone shows that cold and warmed up amps like yours sound noticeably different through loudspeakers. This requires data from blind listening tests performed by the methods established by Toole and Olive.
I think that link is from Floyd E. Toole's book,
Sound Reproduction The Acoustics and Psychoacoustics of Loudspeakers and Rooms. It reviews most of the major findings of his career.
Toole and Olive are the first scientists who systematically examined how to do blind listening tests with humans and audio equipment, and what we could learn with their test results. No good scientist, including Toole and Olive would ever use the words "holy grail of proof". But so far, their work is the gold standard on this subject. It will remain so until others follow up, expanding on their findings, or refuting them.