A single-stage, reciprocating compressor made of conventional cast iron cylinders and forged steel rods, valves, and other gear cannot operate under steady-state conditions compressing atmospheric air to a pressure of 125 psig -- PERIOD. At least, it will only operate long enough to self-destruct.
What HySys doesn't know (because it has no knowledge or expertise in compressing air) is that some single stage compressors are used to produce 125 psig air - either because the owners/operators are too ignorant or cheap to do the correct, economical, and safe operation of doing the operation in a 2-stage machine. What is being referred to here is obviously the ordinary, cheap, car garage where the operator is only interested in producing the 125 air under unsteady state operation - not continous operation. So what is happening is that the machine is stopped and started as the air needs call for it. This may allow the whole system to heat up - but under unsteady state heat transfer: the entire system never reaches the 700 oF (Thank God!). It is certainly not a proper, well-designed and safe system - but it may seem to work to the layperson who only worries about the immediate capital costs. These type of compressor applications don't last very long; they auto-consume themselves with excess heat and wear-tear operation.
HySys will only produce garbage if you input garbage. If you don't advise HySys that this is an unsteady state operation, it can't figure it out because it is too stupid and can't engineer. It depends on YOU to do the engineering.