The CAESAR II hanger selection process collects two values to select your spring - a load and a travel. The stiffness of the spring "candidate" is used with these two values to test min/max loads and load variation.
At this point there is no distinction made on the load used - cold or hot, or, better, installed or operating. It's the (default) hot load or the user-specified cold load.
MSS SP-69 defines a "variability factor" = (travel*k)/Operating Load.
I would call our term "load variation" = (travel*k)/Hgr Design Load.
They may not be the same.