Heat insulation improves indoor comfort and reduces operational carbon emissions by minimising heat loss in the use stage of its life cycle. Amidst the increasing energy efficiency of buildings, the importance of production, construction, and end-of-life stages causing embodied carbon emissions has started to show an upward trend. With the right selection of insulation materials and thickness, the total carbon emissions can be further reduced considering the lifetime of the building. Finding the most favourable option for insulation requires investigating the thermal insulation capacity and the impact generated throughout its production, transportation, implementation, and destruction. This study aims to identify the best possible passive refurbishment scenario in terms of insulation material and thickness for a typical residential apartment in Budapest. The optimisation process is carried out using a genetic algorithm as a Python module, focusing on minimising the whole life cycle carbon emissions. The current Energy Performance Building Directive of the European Union only addresses operational carbon, while considering the whole life cycle of building materials appears only as a recommendation. The demonstrated solution provides insights that can be applied to other cases. The method used has great potential to incorporate other passive and active refurbishment elements, such as optimizing building service engineering systems or additional components of the building envelope.