We present a model of dense Z-Pinch heating. For pinches of sufficiently small diameter and high current, direct ion heating by m=0 instabilities becomes the principal channel for power input. This process is particularly important in the present generation of dense micro-pinches (e.g., HDZP-II) where instability growth times are much smaller than current risetimes, and a typical pinch diameter is several orders smaller than that of the chamber. Under these conditions, m=0 formation is not disruptive: the large E{sub z} field reconnects the instability cusps externally, after which the ingested magnetic flux decays into turbulent kinetic energy of the plasma. The continuous process is analogous to boiling of a heated fluid. A simple analysis shows that an equivalent resistance R{sub t} = {ell}/4{radical}Nm{sub i}({mu}{sub 0}/{pi}){sup 3/2}I/r appears in the driving circuit, where I is the pinch current, N is the line density, {ell} is the pinch length, m{sub i} is the ion mass, and r is the pinch radius. A corresponding heating term has been added to the ion energy equation in a 0-D, self-similar simulation, which had been written previously to estimate fusion yields and radial expansion of D{sub 2} fiber pinches. The simulation results agree well with the experimental results from HDZP-II, where the assumption of only joule heating produced gross disagreement. Turbulent ion heating should be the dominant process in any simple pinch carrying meg-ampere current and having submillimeter radius
