  Interfaces between hot and cold magnetized plasmas exist in various
astrophysical contexts, for example where hot outflows impinge on an ambient
interstellar medium (ISM). It is of interest to understand how the structure of
the magnetic field spanning the interface affects the temporal evolution of the
temperature gradient. Here we explore the relation between the magnetic field
topology and the heat transfer rate by adding various fractions of tangled vs.
ordered field across a hot-cold interface allow the system to evolve to a
steady state. We find a simple mathematical relation for the rate of heat
conduction as a function of the initial ratio of ordered to tangled field
across the interface. We discuss potential implications for the astrophysical
context of magnetized wind blown bubbles (WBB) around evolved stars.
