CERN's Linac4 is a 160 MeV linear accelerator currently under construction. It will inject negatively charged hydrogen ions into CERN's PS-Booster. Its ion source is a noncesiated rf driven H(-) volume source directly inspired from the one of DESY and is aimed to deliver pulses of 80 mA of H(-) during 0.4 ms at a 2 Hz repetition rate. The Superconducting Proton Linac (SPL) project is part of the luminosity upgrade of the Large Hadron Collider. It consists of an extension of Linac4 up to 5 GeV and is foreseen to deliver protons to a future 50 GeV synchrotron (PS2). For the SPL high power option (HP-SPL), the ion source would deliver pulses of 80 mA of H(-) during 1.2 ms and operate at a 50 Hz repetition rate. This significant upgrade motivates the design of the new water cooled plasma generator presented in this paper. Its engineering is based on the results of a finite element thermal study of the Linac4 H(-) plasma generator that identified critical components and thermal barriers. A cooling system is proposed which achieves the required heat dissipation and maintains the original functionality. Materials with higher thermal conductivity are selected and, wherever possible, thermal barriers resulting from low pressure contacts are removed by brazing metals on insulators. The AlN plasma chamber cooling circuit is inspired from the approach chosen for the cesiated high duty factor rf H(-) source operating at SNS.