Increasing the penetration of Variable Renewable Energy (VRE) in electric generation systems is a fundamental goal in reducing greenhouse gases emission. To reduce power fluctuations in electricity networks and avoid curtailment, large-scale energy storages represent one of the most promising solutions. Thermally-Integrated Pumped Thermal Energy Storage (TI-PTES) systems are an interesting technology that can be used for this scope if the heat source adopted for thermal integration can provide significant thermal power. The ocean temperature gradient in tropical areas is an attractive heat source to be coupled with the PTES system to realise efficient electric storage when integrated with an Ocean Thermal Energy Conversion (OTEC) system. In this study, a heat pump refrigerated by the warm tropical surface water uses electricity surplus from VRE to heat an amount of water contained in an end-life cargo ship used as water storage. The system discharges the stored energy through an ORC cycle refrigerated by the cold deep seawater when VRE production is low. A preliminary sensitivity analysis of the storage size and temperature is proposed through detailed system modelling to define the optimal design and layout. Therefore, the part-load analysis of the system is assessed to characterise the off-design performances and evaluate the potentialities of this system when applied to a plausible case study that includes VRE generation and an electric demand profile. Finally, the Levelised Cost Of Storage (LCOS) is evaluated and compared to other storage technologies. Results show that the round-trip efficiency may achieve values higher than 60 %, and an equivalent electric battery capacity of 20 MWh is feasible using end-life ships acting as energy storage. In contrast, the obtained LCOS of 388 €/MWh is still not competitive in the energy market. However, since tropical areas have high energy prices, considering this application for remote island electrification could be an interesting solution.