Greg, having AS pain leave when we are ill is a common effect. Many of us here have experienced this. When our immune systems are focussed on an actual illness, it stops attacking us.
Morning stiffness is a direct result of inactivity, as you say. I have experienced this in the heat of the Caribbean waking up under a light sheet and in the -25 of Northern Ontario under a duvet.
Body temperature may be a factor for you, as may kleb. p., but I can assure you that it is not a factor for me. Nor is it a factor for every ASer.
Light and love,
