Why does 37°C feel so hot when our bodies are at that temperature already?

That’s the temperature of your core. Your skin is usually around 34°C and your face, fingers and toes can be much colder. The receptors in your skin react to differences in temperature, so when you put your hand on your bare stomach, your hand registers warmth but your belly shrieks ‘cold!’, even though both are ‘skin temperature’. Similarly, the inside of your mouth feels warm to your finger, but not to your tongue.