Thermal quantum field theories are expected to obey a relativistic KMS condition, which replaces both the relativistic spectrum condition of Wightman quantum field theory and the KMS condition, which characterises equilibrium states in quantum statistical mechanics. In a previous work it has been shown that the two-point function of the thermal $P(\phi)_2$ model satisfies the relativistic KMS condition. Here we extend this result to general $n$-point functions.