We consider a two-level \(P\sigma _{z}\) pseudo-Hermitian system in contact with a thermal bath to study various thermodynamic properties. The system is realized in terms of infinitely many invariant subspaces. We find explicit solution in each subspace analytically. The quantum system undergoes a \(P\sigma _{z}\)  phase transition in each invariant subspace, when the non-Hermitian coupling exceeds a certain critical value ( \(\mu _c\) ). We calculate various thermodynamic quantities and observe that these quantities show divergences exactly at the exceptional points (EPs) of the theory.