...since nitrogen is an inert gas you not will have the fluctuation in psi when tires warm up. How true is this statement?
That statement is NOT true. All gasses in a confined enclosure will increase pressure when the temperature increases.
What you gain by using nitrogen is that it is "dry" and does not contain the water vapor most air compressors inject into your tires with the air. The water vapor will add to the change in tire pressure as your tire temperatures change. Air, on average, is between 0.5%-1% water vapor. So without a water trap, a compressor will pump some of this water vapor into your tires along with the air.
If the nitrogen fill is free, I'd take it. If it's an extra charge, forget about it.
By the way, regular old air is 78% nitrogen already. :)
~Rick