  Aims: To showcase and characterise the rich phenomenology of temperature
fluctuation patterns that are imprinted on the CMB by the gravitational wave
memory (GWM) of massive black hole (BH) mergers. Methods: We analyse both
individual binaries as well as populations of binaries, distributed in local
cosmological boxes at a given redshift. Results: The magnitude of the
temperature fluctuations scales primarily as a function of binary total mass
and pattern angular scale, and accumulates as a random-walk process when
populations of mergers are considered. Fluctuations of order $\sim 10^{-10}$ K
are easily reached across scales of $\sim 1'$ to $\sim 1^{\circ}$ for realistic
volumetric merger rates of 10$^{-3}$ Mpc$^{-3}$ Gyr$^{-1}$, as appropriate for
massive galaxies at $z=1$. We determine numerically that GWM temperature
fluctuations result in a universal power spectrum with a scaling of
$P(k)\propto k^{-2.7}$. Conclusion: While not detectable given the limitations
of current all-sky CMB surveys, our work explicitly shows how every black hole
merger in the Universe left us its unique faint signature.
