A showerhead for a substrate processing chamber includes: inner walls; an inner plenum between the inner walls; and a faceplate having a first surface and a second surface that is opposite the first surface. Holes through the faceplate extend from the first surface to the second surface. A first inlet is fluidly connected to the inner plenum. A first outer plenum is between the inner walls and outer walls. A second outer plenum is between the inner walls and the outer walls. Coolant: fluidly connect the first outer plenum with the second outer plenum; are located within the faceplate between the first and second surfaces; and are fluidly isolated from the holes. The showerhead also includes a second inlet that is fluidly connected to the first outer plenum.