I have seen many references to the temperature of turkey increasing for a while when resting. This would seem to contradict the first law of thermodynamics.
Not at all.
If we measure the temperature of a “lump of meat” that’s to be roasted, we place the tip of the probe at the center or the thickest part of the roast. Oven temperature is usually way hotter than the temperature we are trying to reach at the core, which means the outside will be nice and crisp (see Maillard reaction).
Meat is a relatively bad conductor of heat, so you get a quite steep temperature gradient, or plainly said, the outside starts browning while the center is still cool. Part of the art of roasting meat is to achieve the balance between juicy and cooked interior and browned, but not burnt exterior.
But back to your question: When you pull your turkey from the oven, it will have the aforementioned temperature gradient. As we all know, this will tend to even out and for the coldest spot (where the probe is), it means getting warmer (while the outer areas get cooler, just as stipulated in the first law of thermodynamics). For a cook, it also means to factor in this so-called “carry-over cooking” and pull the bird slightly before the desired core temperature is reached. Note that in cooking and baking, temperatures of dishes are typically given for the coldest spot.