[VadeRetro]

The falloff of the power spectrum at small scales can be used to determine the temperature of the intergalactic medium (IGM). It is typically 20,000°K, and there is no evidence of evolution with redshift." The term "evolution" is a weasel word for change ( delta ). If the Universe is expanding, the TEMPERATURE should be decreasing adiabatically as space expands, no?

Actually, if you stick out a thermometer into the intergalactic medium, you'd get a reading of nearly absolute zero. There would be very few photons or massive particles contacting the surface of the thermometer. Whatever heat it originally had would simply radiate in the infrared out into the vacuum with very little input to balance the loss.

The same thermometer, anywhere in the universe a few seconds after the big bang, would have been vaporized. In fact, the nucleons would have flown apart into sub-atomic particles, which would have themselves become a quark-gluon like the rest of the universe.

So I guess it depends on what you mean by "temperature."

[VadeRetro]

. . . which would have themselves become a quark-gluon like the rest of the universe.

" . . . become a quark-gluon plasma . . ."