This study presents an evaluation framework for the techno-economic-environmental (TEE) performance of the integrated multi-vector energy networks (IMVENs) including geothermal energy. Geothermal energy storage (GES) offers huge potential for both energy storage and supply and can play a critical role in decarbonising the heat load of smart multi-energy grids. The two most common types of GES, that is, high-temperature GES (HTGES) and low-temperature GES (LTGES), were modelled and integrated within the framework. This framework evaluates the impact of different low carbon energy sources including HTGES, LTGES, wind and Photovoltaics (PV) on the amount of energy imported from upstream, operational costs and emissions of IMVENs to meet the heat load of a region. The evaluation framework performs TEE performance analysis of any configuration of IMVEN representing future energy system pathways to provide a basis for well-informed design choices to decarbonise heat. The TEE evaluation framework was tested on a real-world case study, and several IMVEN configurations were designed and analysed. The results reveal that the most efficient, cost effective and least carbon-intensive configurations for meeting the heat load of the case study are the configurations benefitting from HTGES, from high penetration of heat pumps and from LTGES, respectively. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.