"The third rule of Thermodynamics is: if the average heat energy drops to zero, the Universe is over!"
Seriously, the third of the three laws of thermodynamics is usually stated as a definition: the entropy of a perfect crystal of an element at the absolute zero of temperature is zero. Since heat is a measure of average molecular motion, zero thermal energy means that the average atom does not move at all. Since no atom can have less than zero motion, the motion of every individual atom must be zero if the average molecular motion (heat) is zero.
Thus, if the entire universe had an average heat of zero, the universe (and thermodynamics as well) would be over as far as we're concerned: no motion, no reactions, no observers. If the universe becomes an unobservable motionless system, does it really exist? You can substitute thermodynamics for the Universe in the law if you like.
Tip o' the pen to Ground Control for First law of thermodynamics
and edibleplastic for preliminary wording. (Why this is clever.)