I could quibble with Rich's response...

The spring rate alone does not affect the sustained case loads. It's the preload that does the work here. Normally, the load is balanced in the operating case (hot load design) so the load in the cold case, with its different vertical position, is out of balance. It is this out of balance load that causes the different numbers. These differences are usually low and any large difference would indicate a high load variation on the spring or a very "sloppy" (flexible) system with respect to the magnitude of the hanger load.