I have returned to my office at Monash University in Australia, and can now look up my notes.
At a pump conference in London, I found this empirical formular developed in the South African mining industry, and have changed it into SI units. It applies for water at up to 54 degC:
Efficiency = 100/ [1- (0.003(t -2) + 4160 (TR/TH)] where t is the inlet water temperature, degC, and TR is temperature rise. C deg, and TH is total Head, kPa
I have tried this on high pressure pumps and high water temperatures, and when steam tables are used the results are close.
Mechanical losses are not included, but these are insignifcant for any but very small pumps.