Geometric mechanics is a mathematical framework for investigating dynamical systems arising from Lie group invariant variational principles. An important area where the theory of geometric mechanics is useful is geophysical fluid dynamics. Conservation laws arise naturally in this framework and can be used to classify the structure of fluid models. In this work a hierarchy of models for thermal ocean dynamics is derived within the framework of stochastic geometric mechanics. The ocean models in this dissertation are allowed to have horizontal gradients of buoyancy. As a result, the potential energy in the ocean model has a similar form to potential energy of an adiabatic gas. In this analogy, the buoyancy plays the role of the entropy. This is why ocean models with buoyancy can be referred to as "thermal". The study of thermal ocean models with the framework of stochastic geometric mechanics helps to gain more understanding in how different ocean models with similar structure relate to each other, particularly in the presence of the stochastic parametrisation known as "stochastic advection by Lie transport". By means of dimensional analysis and asymptotic analysis within the framework, a hierarchy of models is derived that permits the usage of stochastic advection by Lie transport. By combining stochastic geometric mechanics, thermal ocean modelling and asymptotic analysis, a tree of related ocean models spanning several spatial dimensions is derived.