We explore the performance of the well-tempered ensemble combined with parallel tempering (PT-WTE) in obtaining a thermodynamical description of a given molecular system. We carefully explain the theoretical procedure employed to extract all the relevant thermodynamical quantities from a PT-WTE simulation. As a specific molecular system, we consider a Lennard-Jones cluster of 147 particles, which is a prototypical case of a finite-size system exhibiting a quasi-first-order phase transition, characterized by a range of temperatures where two distinct phases are thermodynamically stable and coexist. Two separate PT-WTE simulations, which investigate the thermodynamical behavior on different levels of detail, give equally accurate descriptions of the critical phase-coexistence region, indicating the good quality of the PT-WTE results. The positive performance observed here clearly demonstrates that the PT-WTE approach is an effective option when thermodynamical properties are needed.