Display omitted •EMD is used to study the phonon thermal conductivity (PTC), melting characteristics, and tensile strength of both SLGeNR and BiLGeNR.•BiLGeNR exhibits significantly lower PTC than SLGeNR.•PTC of SLGeNR displays an inverse relation with temperature, biaxial compressive strain, and monovacancy defects.•PTC of SLGeNR has been seen to increase gradually with increasing biaxial tensile strain, length and width of the nanoribbon.•BiLGeNR demonstrates high tensile strength and melting temperature compared to SLGeNR. Two-dimensional germanene has provided a cornucopia of new functionalities in the field of nanotechnology owing to its remarkable electronic and thermoelectric attributes. The robust spin–orbit coupling and high carrier mobility give rise to many salient features including non-trivial topological properties, quantum spin-Hall state near room temperature, and topological superconductivity, rendering it an excellent contender for valleytronics, spintronics, and quantum computation. As such, an in-depth characterization of thermal and mechanical properties of germanene is crucial for its practical implication and efficient operation, which remains elusive. Here, we employed equilibrium molecular dynamics simulations utilizing Stillinger Weber potential to reveal the mechanical strength, melting temperature, and phonon thermal conductivity (PTC) of single-layer germanene nanoribbon (SLGeNR) and bilayer germanene nanoribbon (BiLGeNR). Effects of temperature, biaxial tensile and compressive strain, monovacancy defects, length and width of the nanoribbon on the PTC have been rigorously investigated. It has been found that PTC of SLGeNR could be substantially reduced by BiLGeNR. Our simulation results suggest that PTC of SLGeNR demonstrates an inverse relation with temperature, biaxial compressive strain, and monovacancy defects while biaxial tensile strain, length and width of the nanoribbon increases the PTC of SLGeNR significantly. To understand the PTC more profoundly, phonon density of state (PDOS) profiles have been studied. The BiLGeNR demonstrates more tensile strength as well as melting temperature compared to SLGeNR. This study offers a comprehensive guideline for engineering the TC as well as discloses important mechanical and melting characteristics of the SLGeNR and BiLGeNR for a wide range of applications in flexible nano-electronics and thermoelectric nanodevices.