The ubiquitous nature of water invariably leads to a variety of physical scenarios that can result in many intriguing properties. We investigate the thermodynamics and associated phase transitions for a water monolayer confined within a quasi-two-dimensional nanopore. An asymmetric nanopore constructed by combining a hydrophilic (hexagonal boron nitride) sheet and a hydrophobic (graphene) sheet leads to an ordered water structure at much higher temperatures compared to a symmetric hydrophobic nano pore consisting of two graphene sheets. The discontinuous change in the thermodynamic quantities, potential energy (U), and entropy (S) of confined water molecules computed from the all-atom molecular dynamics simulation trajectories, uncovers a first-order phase transition in the temperature range of T = 320-330 K. Structural analysis reveals that water molecules undergo a disorder-to-order phase transformation in this temperature range with a 4-fold symmetric phase persisting at lower temperatures. Our findings predict a novel confinement system which has the melting transition for monolayer water above the room temperature, and provide a microscopic understanding which will have important implications for other nanofludic systems as well.