  We investigate the thermal equilibrium properties of kinks in a classical
$\phi^4$ field theory in $1+1$ dimensions. The distribution function, kink
density, and correlation function are determined from large scale simulations.
A dilute gas description of kinks is shown to be valid below a characteristic
temperature. A double Gaussian approximation to evaluate the eigenvalues of the
transfer operator enables us to extend the theoretical analysis to higher
temperatures where the dilute gas approximation fails. This approach accurately
predicts the temperature at which the kink description breaks down.
