For probably a century now, Foucault pendula have been indoors, so Rowbotham's temperature/sun hypothesis can't apply. Many natural science museums have such pendula indoors, all over the world, and their behavior is well described.
The first part of the wiki is deliberately using data that is over 100 years old, because more recent data exists that contradicts the desired conclusion.
The Mach principle part is just plain wrong. You can distinguish inertial from non-inertial reference points precisely by these sorts of experiments (eotvos effect, coriolis effect, Foucault pendulum, etc.)