Heatwaves are becoming more frequent and severe, intensifying cooling demand and reducing air conditioner efficiencies. This causes peaks in electricity demand that pose operational challenges to power grids. This paper provides methods to mitigate demand peaks and heat stress under heatwaves by jointly adjusting fan speeds and thermostat setpoints in buildings. The methods involve (1) learning baseline models to predict load and thermal comfort, (2) fitting perturbation models that relate fan speed and thermostat setpoint adjustments to perturbations in load and thermal comfort, and (3) optimizing peak load and thermal comfort. The methods are implementable in real buildings, providing fast, accurately predicted optimized solutions that flatten demand peaks and mitigate personal heat stress. This paper demonstrates the methodology through simulation-based case studies of a single building and a six-building neighbourhood. In case studies, the methods reduce peak load by 8-10% while maintaining occupants' thermal comfort within safe and comfortable ranges.