What information does one need to size inrush current limiting resistors?
I suppose to really calculate that you would need:


ambient/body temperature at t0
"disfunction" temperature of the core conductor
temperature/resistance coefficient of the core material
thermal conductivity of the body
thermal capacitance of the body


Of those given I think ther thermal conductivity from the core to the body and inside the body are the most significant. You know e.g. 2W*2,5*5s = 25Ws of power is fine, but that doesn't mean 1s @25W would be fine. You would need to make own measures to get the values that are relevant for your application:

Put the resistor in an oven, measure it's resistance over a few points to determine its temperature/resistance coefficient.

Then power the resistor with a fixed current for a fixed time and immediatly measure the resistance. Double the power, keep the time, measure the resistance and you can calculate the thermal conductivity. The Operating Temp range will give you a hint on how much you can stress the conductor. Add to it the temperature relative to ambient you measured at the resistor core after 2W*2,5*5s and you have the approx max core temperature.

Now you can run some calculations to ensure that your type of load doesn't bring the core to a higher temperature than the manufacturers maximum rated load.

I'm not taking thermal body conductivity or capacity in account, as I assume the time is significantly short.