From MERM, it looks like the function of the Deaerator is basically a high pressure Feedwater heater in mixing both steam and feedwater... The attempt is to bring the mix to a saturated temperature (at pressure) where the gas solubility is zero.
If you can bring water to saturation, then entrained gases want to come out.
Assuming it's working properly, I would think you could almost assume that the exit temp is NEAR saturation (or like) at pressure. Use steam tables to find sat. temp.
If it's more than a ballpark, and you want to confirm that it's working properly, then adiabatic energy balance says:
Mdotwater(enthalpywater) + Mdotsteam(enthalpysteam) = Mdotmix(enthalpymix)
Assuming that it's saturated water, and you know mass fractions, then solve for enthalpy of mix and see if it matches the saturation temp AT the pressure you're operating.
Just a guess. I don't work with these, just attempting to understand what MERM says. Good Luck.