Stress and anger are associated with the [HPA Axis](https://en.wikipedia.org/wiki/Hypothalamic%E2%80%93pituitary%E2%80%93adrenal_axis). Triggering this system releases adrenaline (edit: and cortisol), which cause widening of capillaries in preparation for needing more blood to muscles. Subjectively, the increased rate of blood moving from inside the body to the outside feels warm, because the blood comes from deeper and warmer body parts.
What everyone else said about your body preparing for a fight by increasing blood flow to muscles, but also with a fun fact!
We don’t actually know why your face gets filled with blood (red cheeks) when we are angry, but it is hypothesized that perhaps it is a warning sign to other humans to back off!
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