  The traditional Fourier equation just allows us to study the evolution of
temperature in an "undeformable" bar. The search for its relativistic variant
is a task which is expected to fail because in relativity there are no
undeformable bars. Rigid bodies, in the sense of "as rigid as possible", are
deformables. In this work we show how to write in relativity the system of
equations necessary to study simultaneously deformation and temperature
evolution along a rigid deformable bar. The solutions of the two simultaneous
equations is discussed assuming convenient constitutive relations for the
material. An application is presented.
