It is true that Maxwell [33,
34] had an equation of transfer for the heat flux with a rate term
just as postulated by Cattaneo 80 years later; such an equation
arises naturally in the kinetic theory of gases. However, on both
occasions Maxwell summarily dismisses the term as being small and
uninteresting. He was interested in deriving the proportionality
of heat flux and temperature gradient, Fourier's law. It is
uncertain whether Maxwell was aware of the paradox. But, if he
was, he did not care about it, at least not in the papers cited.
It is conceivable that Maxwell, a prolific writer of letters as
well as of papers, may have mentioned the paradox elsewhere. If
so, the author of this review should like to learn about
it.