Previous research has established that energy demand of buildings in street canyons are affected by the surrounding urban physical characteristics. This suggests that it is possible to optimise the energy performance of buildings by acting on the physical urban parameters that potentially influence their overall energy consumption. Unfortunately, few studies have addressed this issue. Precisely, improving buildings thermal behaviour and energy demand pattern throughout sensitivity-based optimisation by focusing on the building’s envelope design without neglecting the effect of urban context, remains a relatively under-explored research topic. The present study attempts to fill this gap by implementing a combined method based on sensitivity analysis and multi-objective optimisation of energy demand and thermal comfort for an existing residential building subjected to hot arid climatic conditions. The proposed method utilises Latin hypercube sampling with multivariate multiple linear regression to identify the relative importance of design parameters on building performance criteria, namely, the annual energy demand and the integrated summer thermal discomfort. Non-dominated sorting genetic algorithm II (NSGA-II) is then applied to simultaneously optimise the investigated building performance criteria with regards to the identified relevant envelope parameters. The results of sensitivity analysis indicate that window characteristics, thermal insulation, and roof reflectance are the most influential factors. The optimisation results, in turn, show promising improvement potential with a wide range of design solutions that can ensure better energy performance as well as better thermal comfort. The annual energy demand could be significantly improved by 13.2% up to 49.5% while discomfort degrees could be decreased by over 26%.