Where in the body is blood heated to 37C (or whatever the correct temperature is)?

Most body heat is generated in the deep organs, especially the liver, brain, and heart, and in contraction of skeletal muscles.

Most all processes in the body require energy and as that energy is used a slight amount is lost as heat. That happens in every cell of your body and in civilized humans we rather have to get rid of excess heat in those ways you are familiar with. The immediate source of energy for the body is ATP which has three phosphate groups tied together. The energy requiring reactions get a spark of energy when the terminal phosphate group pops of and that spark provides energy but a small amount "sparks" out into the cell and that is what keeps us warm...it is the inefficiency that provides the extra heat we need to keep us at operating temperature.