Decarbonising energy used for space heating and hot water is critical for reaching emission targets. Modelling of thermal energy decarbonisation becomes increasingly complex as additional technology options are included. Spatial aspects become increasingly important when considering heat transport, for example using district heating. This study develops a model for heating energy decarbonisation that makes use of a techno-economic model applied to a large geographic area (Western Switzerland) at high spatial resolution. Global sensitivity analysis is applied to quantify the variance characteristics of the model. Heating energy services provided by retrofits, decentralised heat pumps, and thermal networks are considered. Final energy demand reductions ranges of 70–80% and emissions reductions of 90% were found with levelized costs of providing the heat service of 0.14–0.22CHF/kWh. High sensitivities were found with respect to efficiency parameters (retrofit potentials and seasonal performance factors). The spatial distribution of costs and sensitivities was shown to be highly variable, with a strong correlation with building density. This raises important questions, notably on equitable distribution of energy transition costs.