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The possible inadequacy of temperature as commonly used in thermodynamics is suggested by Truesdell on the basis of theoretical considerations. The M'pemba effect provides stark experimental relevance to his remarks.

In one famously hacked email climate researcher Kevin Trenberth said "We're simply not tracking where the heat is going". The same could be said concerning the M'pemba effect. One may venture to guess that the two problems are not unrelated.

Laws and models

Some readers may agree with the view that laws are man-made rules to regulate human behaviour ("Lex est quod populus iubet atque constituit" i.e. "the law is what the people order and establish" as Gaius put it). Others may regard laws as god-given. Actually the modern idea of physical law was introduced by a deeply religious thinker who regarded his work in theology as not less relevant as, and indeed intimately related to, his formidable contribution to natural philosophy. Nowadays laws are widely regarded as anthropic constructs. Yet there is a deep reluctance to view the physical laws of yore as anthropic rules that we use to build models that describe, organize, relate, extrapolate and, ideally, predict some of our perceptions. The religious background is still there, deeply embedded into the currently fashionable metaphysical objectivism, underlying the authority of the so-called scientific community (consider e.g. the respective impact of the statements: "the purported effect would violate the laws of physics" - "our customary models appear inadequate to describe the purported effect").

NB. The seed for the above "law vs. model" argument was provided by a remark that I heard a few years ago after a conference by Rovelli and others at the FestivalFilosofia in Modena. I remember that its author was an aeronautcal engineer and that at first I found his intervention deeply irritating. Yet it bore fruit.