They will. So, you may need to look at a slower rate of change or the like. Also, any instant cut off could cause the solution to oscillate: turning the flow off could trigger the temperature to rise & turn the flow back on, then off as the temperature drops in the next time step.
Have a look at feed forward and feed back control theory: all I remember from my Uni course is that you spec out the valves etc to withstand the pressure and material (corrosion resistant etc) then find a specialist!
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