Thanks for the challenge, CJ... I think I have an answer for you, but I have to honest and tell you that I had to get the wiring diagrams out to refresh
my decaying brain cells
I think it is important to recognize that in the second case (QRH2) the demand pump has failed to _automatically_ supplement the SYSTEM (total) pressure when the engine pump pressure (we assume) has dropped below 1400psi (GE engines logic value only).... hence the "HYD PRESS _SYS_" msg. In the QRH procedure, we are bypassing the automatics by selecting the demand pump to ON. Note: The SYSTEM pressure sensor is different from the EDP pressure sensor and is the one which puts up the EICAS msg (as well as illuminates the overhead SYS fault light).
In the first case (QRH 1), there is nothing wrong with the automatics.... You "just" have an overheat problem, which, I was told recently, will be generated by a faulty engine pump in most cases.
Hope this makes sense??? (It's a lot easier to understand this stuff with pictures in front of you)
Cheers.
Q.