Though they can produce a similar effect (faster reaction rate), heat doesn't act as a catalyst.
Reaction rate is dependent on how often reagents can overcome the activation energy of a reaction. Therefore, a lower activation energy, $E_\mathrm{a}$, means a faster reaction.
A catalyst lowers the activation energy of a reaction by producing lower energy transition states. This is how catalysts speed up reactions. A generic version of this is shown in the image below. Transition states occur at the local maxima of the graph in this image.
Heat, on the other hand, increases the average kinetic energy of the molecules within a system (i.e. most molecules are moving more quickly). By doing this, the chances of two particles colliding and having enough energy to react are higher because the particles will move faster. Therefore, they will collide more often, and when they do, they will have more "momentum" (so to speak) to get over this energy hill. By making it so more of the reactant particles can overcome this activation energy, heat also speeds up reactions.