velocities and their kinetic energy density are boosted by the underlying lattice vibrations. We consider this effect in a representative transmon comprising two semi-circular superconducting charge islands joined by a Josephson junction. In particular, we solve the Fourier transform of a two-dimensional radial current density having inversion symmetry. The resulting spectral density is ohmic but also scales quadratically with the critical current I_c and logarithmically with the size of the transmon: J(w) ~ I_c^2 w log(kR). We make positive-definite Born-Markov approximations in a generalized Fermi’s Golden Rule and estimate the phonon-induced dephasing rate is negligible compared to current experiments.