Quantum-chemical calculations at several levels of theory were used to assess the stability at different temperatures of a set of 13 binary and ternary Pocontaining molecules that could possibly be formed in an environment with lead, bismuth, oxygen and water. These are conditions that are relevant for a heavy liquid metal cooled fission reactor. The conclusions are that especially PoPb, PbPoO and PoOH and to a lesser extent Po 2 and PoO are stable. These small molecules are likely to be found near the Lead-Bismuth-Eutectic (LBE) coolant at operational temperatures. In contrast Po 3 and PoBi are unlikely to be present under the assumed conditions. Several stability criteria, such as the dissociation into free atoms or into molecular fragments at realistic Poconcentrations or in the thermodynamic limit are discussed at different temperatures. The results obtained with a medium level of theory (Density Functional Theory, PBE0 with Relativistic Effective Core Potentials) show good qualitative correspondence with calculations performed at a much higher level of theory (Multi Reference Configuration Interaction, with spin-orbit coupling and scalar relativistic Hamiltonian). This makes the medium level of theory to be a fair alternative, for obtaining at least qualitative insight, for a high level calculation method which is unfeasible for much larger systems.