We extend our lattice QCD potential based study [1] of the in-medium properties of heavy quark bound states to P-wave bottomonium and charmonium. Similar to the behavior found in the S-wave channel their spectra show a characteristic broadening, as well as mass shifts to lower energy with increasing temperature. In contrast to the S-wave states, finite angular momentum leads to the survival of spectral peaks even at temperatures, where the continuum threshold reaches below the bound state remnant mass. We elaborate on the ensuing challenges in de fining quarkonium dissolution and present estimates of melting temperatures for the spin averaged chi(b) and chi(c) states. As an application to heavy-ion collisions we further estimate the contribution of feed down to S-wave quarkonium through the P-wave states after freezeout.