Sorry that I've been away from this thread...I went back and looked at the datasheet that I linked above. I am quite certain that the 'time constant' value is the thermal time constant for the device temperature to respond to ambient air temperature changes, or similarly the time constant for the device to cool down in air when power is taken away. This is not the 'warm up' time when the device is turned on.
Think about it; these devices would be _useless_ for their intended task of limiting inrush current in power supplies if they took a minute to 'warm up'; could you imagine plugging your computer in and having to wait a minute for the green light to come on...windoze is bad enough /ubbthreads/images/graemlins/smile.gif
These devices have a mass of perhaps 1 gram, and when you first turn them on they will be resistive heaters generating several watts of heat. The will heat up _quite_ rapidly. Figuring out how rapidly is another, more difficult problem. You would need to know the 'heat capacity' of the device (essentially how many Joules or Calories it takes to raise the device's temperature), you would need to know the operating temperature of the device, and you would need a model of your power supply and load.
I believe that one could figure out the heat capacity from a combination of the dissipation factor and the time constant; imagine the device is an RC circuit. The analog of charge in the capacitor is heat in joules, the analog of conductance (inverse of resistance) in amps/volt is the dissipation in W/°C, and the analog of volts is temperature difference in °C.
I can't follow this up further at the present time, but it should give you some ideas.
-Jon