  Motivated by the recent heat transport experiments in 2D antiferromagnets,
such as La$_2$CuO$_4$, where the exchange coupling $J$ is larger than the Debye
energy $\Theta_{\rm D}$, we discuss different types of relaxation processes for
magnon heat current with a particular focus on coupling to 3D phonons. We study
thermal conductivity by these in-plane magnetic excitations using two distinct
techniques, Boltzmann formalism within the relaxation-time approximation and
memory-function approach. Within these approaches, a close consideration is
given to the scattering of magnons by both acoustic and optical branches of
phonons. A remarkable accord between the two methods with regards to the
asymptotic behavior of the effective relaxation rates is demonstrated.
Additional scattering mechanisms, due to grain boundaries, impurities, and
finite correlation length in the paramagnetic phase, are discussed and included
in the calculations of the thermal conductivity $\kappa(T)$. Again, we
demonstrate a close similarity of the results from the two techniques of
calculating $\kappa(T)$. Our complementary approach strongly suggests that
scattering from optical or zone-boundary phonons is important for magnon heat
current relaxation in a high temperature window of $\Theta_D\lesssim T \ll J$.
