Very often CESAR get’s a little bit lost designing spring hangers, .....
Sounds like user error. CAESAR designs my springs exactly as I tell it too.
If you want zero dead weight displacements, choosing
Cold Load Deisgn will get you pretty close.
Hot Load design is used most often because it supports the optimum weight load when the system is hot and operating rather than when it's cold.
I also use the
Center Hot Loads option so CAESAR chooses the spring with the hot load nearest the center of the load range. You can also adjust the variability on a particular spring to force CAESAR into giving you a softer spring (longer movement range) and it'll reduce the difference between your hot and cold loads.
This is all covered in detail in the CAESAR manuals and help sections.
Normally small deflections at your spring supports in your weight case is acceptable