  A surprising "planar" thermal Hall effect, whereby the field is parallel to
the current, has recently been observed in a few magnetic insulators, and this
has been attributed to exotic excitations such as Majorana fermions or chiral
magnons. Here we investigate the possibility of a planar thermal Hall effect in
three different cuprate materials, in which the conventional thermal Hall
conductivity $\kappa_{\rm {xy}}$ (with an out-of-plane field perpendicular to
the current) is dominated by either electrons or phonons. Our measurements show
that the planar $\kappa_{\rm {xy}}$ from electrons in cuprates is zero, as
expected from the absence of a Lorentz force in the planar configuration. By
contrast, we observe a sizable planar $\kappa_{\rm {xy}}$ in those samples
where the thermal Hall response is due to phonons, even though it should in
principle be forbidden by the high crystal symmetry. Our findings call for a
careful re-examination of the mechanisms responsible for the phonon thermal
Hall effect in insulators.
