More work and bigger function require more power which in turn generate more heat. Video needs scanning of APSC sensor which requires power and so produces more heat. Therefore, using VF instead of LCD helps to reduce consumption of power and heat and retracting LCD
away from the camera body provides ventilation.
There are a few things that can be done to help. Maybe they shoot short takes and switch off live view in between takes. Maybe they have more than one camera so they can let the hot one cool down and continue shooting on another camera. Maybe they use a battery grip instead of internal battery, which reduces the amount of heating. Maybe they shade the camera from the sun when shooting outdoors.