Since $\langle (A+a) - \langle (A+a) \rangle \rangle = \langle A - \langle A \rangle \rangle$ do we care if $A$ is a temperature or a temperature anomaly?

Numerically, I think $\langle A B \rangle - \langle A \rangle \langle B \rangle$ is a bad way to the computation if $A$ and $B$ tend to be big.