Urban energy poverty remains a critical challenge affecting millions worldwide, with significant implications for socio-economic development and sustainability. This study employs Monte Carlo simulations to analyze the variability in energy poverty, as measured by the Multidimensional Energy Poverty Index (MEPI). Through this approach, we explored how different socio-economic predictors affect MEPI scores across five scenarios: economic growth and diversification, energy transition and technological innovation, climate change impacts and vulnerability, policy intervention and social safety nets, and stagnation and rising inequality. The sensitivity analysis revealed that household income, size, and food security are paramount in influencing urban energy poverty levels. Scenarios involving economic growth and technological innovation demonstrated positive impacts on reducing energy poverty, while scenarios of climate change and economic stagnation highlighted the vulnerabilities and widening disparities within populations. The results suggest that to effectively alleviate urban energy poverty, policy interventions must be comprehensive, targeting the identified influential factors. The study emphasizes the need for targeted policy interventions on social safety nets to alleviate energy poverty.