What advantage does an enzyme serve over catalysis by the addition of heat energy?
Enzymes have two benefits over raising the temperature:

First, reducing the activation energy by reusable enzymes is far more energy-efficient, apart from the fact that the required temperature would vary for different reactions.

Second, enzymes are able to be controlled by allosteric mechanisms, which facilitates metabolic control by feedback loops, feedforward motivs and receptor-mediated processes. In the example of glycolysis this enables the cell to fine-control its supply with energy equivalents (see figure from Wikimedia Commons below). This mechanism may be the most important function of enzymes.



Reference


William C. Plaxton: Principles of Metabolic Control. In Kenneth B. Storey (ed.): Functional Metabolism: Regulation and Adaptation, John Wiley &amp; Sons, Inc. 2004