We study an extension of the gravity dual to a perfect fluid model found by Janik and Peschanski. By relaxing one of the constraints, namely invariance under reflection in the longitudinal direction, we introduce a metric ansatz which includes off-diagonal terms. We also include an $R$-charge following Bak and Janik. We solve the Maxwell-Einstein equations and through holographic renormalization, we show that the off-diagonal components of the bulk metric give rise to heat conduction in the corresponding CFT on the boundary.

13 pages, v2: expanded discussion incl. R-charge