  The "regular" model presented here can be considered to be the most natural
solution to the problem of constructing the simplest possible relativistic
analogue of the category of classical Fourier--Euler thermally conducting fluid
models as characterised by a pair of equations of state for just two dependent
variables (an equilibrium density and a conducting scalar). The historically
established but causally unsatisfactory solution to this problem due to Eckart
is shown to be based on an ansatz that is interpretable as postulating a most
unnatural relation between the (particle and entropy) velocities and their
associated momenta, which accounts for the well known bad behaviour of that
model which has recently been shown to have very pathological
mixed-elliptic-hyperbolic comportments. The newer (and more elegant) solution
of Landau and Lifshitz has a more mathematically respectable
parabolic-hyperbolic comportment, but is still compatible with a well posed
initial value problem only in such a restricted limit-case such as that of
linearised perturbations of a static background. For mathematically acceptable
behaviour undermore general circumstances, and a fortiori for the physically
motivated requirement of subluminal signal propagation, only strictly
hyperbolic behaviour is acceptable. Attention is drawn here to the availability
of a more modern "regular" solution which, is fully satisfactory as far as all
these requirements are concerned. This "regular" category of relativistic
conducting fluid models arises naturally within a recently developed
variational approach, in which the traditionally important
stress--momentum-energy density tensor is relegated to a secondary role, while
the relevant covariant 4-momentum co-vectors are instead brought to the fore.
