  We study the dynamics of the three-dimensional polaron - a quantum particle
coupled to bosonic fields - in the quasi-classical regime. In this case the
fields are very intense and the corresponding degrees of freedom can be treated
semiclassically. We prove that in such a regime the effective dynamics for the
quantum particles is approximated by the one generated by a time-dependent
point interaction, i.e., a singular time-dependent perturbation of the
Laplacian supported in a point. As a by-product, we also show that the unitary
dynamics of a time-dependent point interaction can be approximated in strong
operator topology by the one generated by time-dependent Schr\"{o}dinger
operators with suitably rescaled regular potentials.
