We present a new method to study the Nernst effect and diamagetism of an extreme type-II superconductor dominated by phase fluctuations. We work directly with vortex variables and our method allows us to tune vortex parameters (e.g., core energy and number of vortex species). We find that diamagnetic response and transverse thermoelectric conductivity ($alpha_{xy}$) persist well above the Kosterlitz-Thouless transition temperature, and become more pronounced as the vortex core energy is increased. However, they textit{weaken} as the number of internal vortex states are increased. We find that $alpha_{xy}$ closely tracks the magnetization $(-M/T)$ over a wide range of parameters.
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