How does the heat energy transfer from inside you to the surface of your skin?

Energy is not a physical unit. It is a philosophical concept and an accounting technique used to analyze mechanical and chemical exchanges. In nuclear physics it is defined as a wavelength of light, in biology it is a synonym for metabolism, and in public utilities they say energy when they mean connectivity. Anybody who uses the word in any other context either does not know what he is talking about, or is peddling something you don't need.

The biggest contributor to cooling the body is the blood. It carries heat evenly to all parts. Heat is then removed by evaporating moisture in the lungs, by convection on the skin (that means a breeze), and by evaporating sweat.