Ann: Alexium Alexicool Treated Pillows Provide Superior Cooling, page-43

The thing with PCM is that you will still wake up with a sweaty pillow in the conditions you describe. It absorbs a small amount of heat initially, until it reaches capacity, at which point it effectively becomes a normal pillow. If the room temperature is high like you describe then it will already have reached its capacity before you go to bed so will be totally useless...
If the temperature is moderate then it will provide a heat absorption effect - which is the cool to the touch sensation - until it reaches capacity. This will only take a short amount of time, as indicated by the inhouse research, then it effectively becomes a normal pillow once again. It will feel nice at the beginning but won't stop the pillow becoming sweaty over the course of the night any more than your average pillow does.

It certainly won't be changing anyones life - AJX holders inclusive.