Stupid question: Is is safe to add water (room temperature) to the filler neck while the car is fully warmed up? I'm not concerned about getting burned my coolant, but rather warping the housing due to change in temperature. Should I let the car cool down first? Thanks in advance.

 

as long as there is water already in the engine it won't hurt anything, but if you're that concerned you can just fill the overflow tank to full with the water and leave the fill cap on the pump neck and the water will get pulled into the system as needed.