The process of thermal conduction is what caused you to sense the heat.
Temperature is a measure of the rate of molecular oscillation, and adding energy to an atom will make it hotter. The high-energy soup will lose the extra energy to the bowl, resulting in the slowing of the soup molecules but the consequent increase in speed of the molecules of the bowl. This would continue until the rate of the bowl atoms is equal to those of the soup, or until the temperatures are equal.
