so the PCM pillow will conduct the 37 degree heat away from the...

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 .

Not quite, when the PCM is being activated the temperature of the pillow doesn't rise, even though its absorbing heat. So while the PCM is active the heat conduction slows, the heat energy is rather being used to transition the phase change. If its conducting heat it means the phase change isn't working. Once the PCM is at capacity the pillow then conducts like any other pillow. PCM doesn't help with conductivity. I have a physics degree, so you can trust me on this one. If you want to design a conductive pillow you can do it without PCM, though PCM might help with the marketing.

When the surrounding temperature rises from below to above the PCM activation range, it absorbs heat energy. When the surrounding temperature falls below the acitivation range it releases that heat energy.
Its completely analogous to water boiling. Once water reaches 100 degrees, the temperature stops rising and heat is instead used to transition the water from liquid to steam. Its still absorbing the heat energy, but the temperature isn't rising.