  We investigate the thermal equilibrium properties of kinks in a classical
$\F^4$ field theory in $1+1$ dimensions. From large scale Langevin simulations
we identify the temperature below which a dilute gas description of kinks is
valid. The standard dilute gas/WKB description is shown to be remarkably
accurate below this temperature. At higher, ``intermediate'' temperatures,
where kinks still exist, this description breaks down. By introducing a double
Gaussian variational ansatz for the eigenfunctions of the statistical transfer
operator for the system, we are able to study this region analytically. In
particular, our predictions for the number of kinks and the correlation length
are in agreement with the simulations. The double Gaussian prediction for the
characteristic temperature at which the kink description ultimately breaks down
is also in accord with the simulations. We also analytically calculate the
internal energy and demonstrate that the peak in the specific heat near the
kink characteristic temperature is indeed due to kinks. In the neighborhood of
this temperature there appears to be an intricate energy sharing mechanism
operating between nonlinear phonons and kinks.
