The service manual will tell you the temperature specs, but mine doesn't give details on cooling water flow pressure. On my F50, the fully-open temperature for the thermostat is 158F. So it's expected to run at least 158F.
The way to confirm if the water pump is pumping water properly is to fast-idle it and look at the exit stream. If it's not stiff and strong, that means you have an issue with the impeller or a blockage in the cooling lines.
Again, the thermostat is cheap to replace. But really, I suspect the impeller or something about the water pump assembly is not right. What part number did you buy?