Thermal properties and structures of the water cluster containing fifteen molecules, either pure or doped with methane, are studied via classical parallel tempering Monte Carlo calculations in the isothermal-isobaric ensemble. The main emphasis is on structural transformations the cluster undergoes with increasing temperature and pressure. A simple TIP4P interaction model is employed for water and the unified-atom approximation with a Lennard-Jones potential is used to model the methane-water interaction. The results are compared with the data obtained recently for zero temperature via evolutionary algorithm calculations [Hartke, J. Chem. Phys., 2009, 130 art. no. 024905].