Liquefied natural gas (LNG) demand is rising globally, with LNG tanks facing instability and safety risks during storage and transportation. The study investigates the LNG rollover behavior under marine conditions by developing a three-dimensional Computational Fluid Dynamics (CFD) model that integrates phase changes, temperature and composition diffusion. The Volume of Fluid (VOF) method is employed, along with UserDefined Functions (UDFs) and mesh motion, to simulate tank motion, validated against relevant sloshing experiments. The analysis explores the coupling effects of heat transfer and sloshing in membrane LNG tanks under roll, pitch, yaw, and combined excitations, elucidating the driving mechanisms of rollover. The results indicate that reducing the sloshing periods and increasing amplitudes accelerate LNG motion, deform the stratified interface, enhance mixing and heat transfer, and advance rollover onset. Roll and pitch excitations significantly affect rollover compared to yaw. Under combined roll and pitch excitations, rollover initiation time was 28 % earlier, with a 30 % increase in evaporation rate compared to roll excitation. In static conditions, LNG rollover is primarily driven by double-diffusion convection, whereas sloshing is governed by dynamic effects. The study highlights the critical role of integrating sloshing excitation effects in the design of LNG storage and transport systems.