Why does your ears get hot?

Because the rest of your body is feeling hot. When you feel hot, the capillaries (small blood vessels) in your ears dilate, or spread out, so that more heat can escape from the blood.

Sometimes, when you feel embarrassed, your body is under stress, from muscle action and various substances released from your glands due to your body's reaction to that emotion. This causes the same thing as when you feel hot to happen, and your capillaries in your ears, and sometimes your face, dilate, causing a rush of warm blood to reach those areas.