Arc volcanism at subduction zones is likely regulated by the mantle wedge's flow regime and thermal structure and, hence, numerous studies have attempted to quantify the principal controls on mantle wedge conditions. In this paper, we build on these previous studies by undertaking a systematic 2-D numerical investigation into how a hydrated rheology and thermal buoyancy influence the wedge's flow regime and associated thermal structure. We quantify the role of a range of plausible: (i) water contents (0–5000 H/106Si); (ii) subduction velocities (2–10 cm/yr); and (iii) upper-plate ages (50–120 Myr), finding that small-scale convection (SSC), resulting from Rayleigh-Taylor instabilities, or drips, off the base of the overriding lithosphere, is a typical occurrence. The morphology of SSC varies with viscosity and subduction parameters, with drips at their most prominent when subduction velocities and wedge viscosities are low. Our results confirm that high subduction velocities and wedge viscosities promote a dominantly corner-flow regime, and strong upper-plate erosion below the arc region. By contrast, we find that back-arc upper-plate erosion by SSC is largely controlled by wedge viscosity, occurring when: (i) viscosities are < 5·1018 Pa s; and (ii) the length of the upper plate, available for destabilization, exceeds the characteristic wavelength of instabilities. Thus, if hydrous weakening of wedge rheology extends at least 100–150 km from the trench, our 2-D models predict an unstable flow regime, resulting in temperature fluctuations of 50–100 K, which are sufficient to influence melting and the stability of hydrous minerals.