  We propose a causal heat conduction model based on a heat kernel violating
the fading memory paradigm. The resulting transport equation produces an
equation for the temperature. The model is applied to the discussion of two
important issues such as the thermohaline convection and the nuclear burning
(in)stability. In both cases the behaviour of the system appears to be strongly
dependent on the transport equation assumed, bringing out the effects of our
specific kernel on the final description of these problems. A possible
relativistic version of the obtained transport equation is presented.
