Our body generally stores its biological energy in the form of matter. That's food in your tummy, blood sugar in your blood, fat on your hips etc.. It needs to be brought to a chemical reaction to be turned into physical energy, which generally happens ad-hoc. This biological energy decays like the rest of your body.

And then a tiny bit of physical energy is always present in your body:

• Potential energy: You'll collapse and transfer it as movement energy into the ground, where friction will turn it to heat.
• Movement energy: You might be swinging your arm as you die. It will likely bump into another object or your body and also be turned into heat by friction.
• Electromagnetic fields: Your brain cells and nerves will be blasting lightnings at each other. Those will fizzle out within a few moments, and again turn into from the friction of the electrical resistance where they impact.
• Heat: The heat from these other processes, as well as your general body heat, is transferred to its surroundings via conduction and infrared radiation.