Bob Shuman wrote:

More importantly, if I wanted to beef up this part to prevent this
from happening again, what generic parameters should I be looking for
in a thermistor at the local RS store? The 5 ohms and .18 ohm are a
good place to start, but I did not see any type of current limit or
power rating (assuming the .18 ohms) for the device.

If it is a 600W non-PFC power supply we might assume at 80% efficiency
the input power to be somewhere around 750W.

750/120 = 6.25A (sound familiar) - full power operation.

Per Ohm's Law: 5 ohm starting resistance = 31W if starting inrush is
100% of full power load (not likely).
..18 ohm ending resistance = 1.125W at full power.

Note that the inrush current limit for the 5D-9 is only 3A, so either
you don't have a 600W supply or (most probably) the max starting surge
is calculated at 50% of the full power load or perhaps as you stated the
device is underrated. You decide.