Ann: Alexium Alexicool Treated Pillows Provide Superior Cooling, page-52

Body temperature is around 37 degrees C , if you are on an insulated pillow the head to pillow surface becomes close to 37 degrees , I think we would all agree that is an uncomfortable room temperature - just like being in a pool over about 27 degrees C .
As humans we find comfort in temperatures below our body temperature guessing around 2o degrees
Would not the PCM pillow by design be a conductor of heat rather than being an insulated pillow, so the PCM pillow will conduct the 37 degree heat away from the body and release the heat to closer to the ambient room temperature and keep the head cooler, similar to touching a steel ship railing which stays cool right up to about 30 degrees (if out of the sun ) while a wooden (insulated railing ) feels warm .
Therefore the pillow does not get to capacity as you assert (ie act as a heat sink without an outlet for the heat and stops when it reaches capacity ) , instead it releases the heat to the environment continually .
Mind you your assertion falls down in logic in the first sentence when you mention "it absorbs a small amount of heat " as to absorb heat it must have lost heat in the past , which means the pillow is not a closed loop system .