Perturbations propagating perpendicularly to a zero-order gradient direction are studied in an inhomogeneous β ≫ 1 plasma. (Zero-order temperature, density and magnetic-field gradients are assumed to be parallel.) Coupling between hydrodynamic motion, thermal waves and magnetic-field evolution yields four modes of oscillation. The case of zero initial magnetic field extends previous results by inclusion of hydrodynamical effects. In the case of a magnetically insulated wall-confined plasma (ωeτe ≫ 1, β ≫ 1), some of the modes can be driven unstable. An upper limit on gradients is given for such wall-confined plasmas to be stable. The connection with anomalous β ≫ 1 transport is briefly discussed.