I've interpreted "beer temperature" to be the highest temperature the beer has gotten after fermentation completed and before bottling.
The reason this temperature is even important is that there will be some CO2 in the beer before bottling, so when priming, only enough sugar is needed to get you to a level of CO2 between your desired final volume of CO2 and what's already in the beer before bottling.
While fermenting, though the vast majority of CO2 escapes out of the airlock, some CO2 remains in suspension. The cooler a liquid is, the more gas it can hold; the warmer it is, the less it can hold.
Once fermentation has completed and no more CO2 is produced, the CO2 already produced will suspend in the beer. If the beer gets warmed up, then some of the CO2 will escape the liquid. Even if the beer gets cooler after this, CO2 won't necessarily go back into solution because the CO2 has already escaped and no more is being produced within.