We have studied the impact of target material on the electron temperature of high power impulse magnetron sputtering (HiPIMS) discharges. The study is based on results from modeling 35 discharges with seven different target materials, using the ionization region (IR) model, a global plasma chemistry model for HiPIMS discharges. We find that the typical evolution of electron temperatures during a HiPIMS pulse stabilizes at the end of the pulse as a result of a balance between electron heating and electron collisional cooling. The underlying cause is a self-regulating mechanism: the monotonically increasing rate coefficients for relevant electron temperatures in HiPIMS discharges ensure that a higher electron temperature enhances electron collisional cooling, while a lower electron temperature reduces it. We furthermore find the steady state electron temperature to be inversely correlated to the sputter yield of the target material. This is a result of the atomic composition in the IR shifting from argon-dominated at low sputter yields to metal-rich at high sputter yields. As the metal ionization rate coefficients are larger at lower electron temperatures compared to that of the argon ionization rate coefficient, the self-regulating mechanism maintains a lower electron temperature in metal-rich discharges. This has implications for the metal ion escape in a HiPIMS discharge, since the ionization mean free path of sputtered atoms depends on the electron temperature. As a result, ionization in metal-rich discharges (lower electron temperature) occurs, on average, further away from the target surface, where the remaining potential hill to climb, in order for a metal ion to escape to the bulk plasma, is lower. Metal ions in those discharges can therefore escape more easily to the substrate region compared to metal ions in argon-dominated discharges.