The achievement of national pledges that are compatible with the Paris Agreements warming limit of 1.5C is a massive challenge, as it requires not only an acceleration of technological innovation, but also a socio-economic and cultural transformation. Reducing uncertainties demands a better integration of behavioural evolutions in models exploring future energy pathways, including non-monetary barriers and drivers to technology diffusion. This study provides suggestions on incorporating social mechanisms of change such as resistance to change and the diffusion of environmental values into a UK-focused probabilistic energy system model, with a focus on people's attitudes towards residential heating technologies. We also offer a comprehensive literature review on interdisciplinary energy transitions modelling and exploratory scenarios embedding climate risks perceptions. We argue that efficient policy-making to meeting net-zero emissions targets must fully embrace whole-system approaches, support the more constrained segments of society, and account for interconnected socio-political factors.