I set my tires at 36# front and 33# rear cold pressure as per the door jam sticker. When I first drive the car the TPMS display indicates that I have 34# in the front and 31# in the rear. Oddly (to me) both are exactly 2# less than what my tire pressure gauge shows. I purchased a new tire pressure gauge thinking that my old gauge might be a fault, and the results are the same. Is this a known issue, just the way it works or do I just have a special car?

The tire pressure display does indicate higher pressures as the tires heat up.

The sensors are usually good to better than +/- 1 psi, so unless you have NIST-certified tire gauges, I'd say it's more likely both your gauges are off than that the sensors are. Gaining a few psi as the tires heat up is perfectly normal, I've seen the wife's Altima gain as much as 5 psi on a long trip in hot weather that started out in a cool morning driveway.