With the increasing focus on sustainable energy solutions and national net-zero emissions goals, repurposing of abandoned underground mines for thermal energy storage has the potential to make significant impacts. The international Geothermica consortium, Galleries to Calories (G2C), is investigating the potential for storing waste heat from a supercomputing facility in abandoned, flooded coal mines southeast of Edinburgh, Scotland. The system termed the Geobattery or GeoTES involves injecting heat into mine workings, conveying it using regional groundwater flow, and then using the stored thermal energy for district heating and cooling via heat pumps. The Edinburgh site is unique due to the connection of three individual collieries that are linked by underground roadways and hydraulically conductive coal seams, thus enabling heat to be readily stored and transported over several kilometers. The internal structure of collieries poses challenges due to their partially unknown internal structure, involving fully excavated seams, partially mined pillars, open and collapsed tunnels, and unmined rock formations. To address these uncertainties, we propose to use a multi-level stochastic modeling approach using the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE). Our team has developed a preliminary and geometrically simplified numerical model that focuses on the main coal seams. These seams are further subdivided into multiple subdomains so that they can be discretized individually. Initially, a stochastic analysis involving many thermo-hydraulic simulations is conducted to identify promising bulk parameter combinations that replicate field observations. Once these parameter combinations are determined, the model is extended in a second phase to incorporate the geomechanical effects associated with various operational conditions of the Geobattery. This extension facilitates the necessary evaluation of heat plume migration and stress field changes, critical for assessing the mechanical stability of the collieries and heat losses that may occur during the operation of the Geobattery.