No, heat is not a conserved quantity.

A conserved quantity remains the same before and after the physical event.

Heat is a form of energy, and energy can neither be created nor be destroyed, but can transform from one form to another.

Best example is a thermocouple, where heat energy is transformed into electrical output due to adjoining two dissimilar metals.

From 1st principle of thermodynamics, only the total energy before or after transformation remains constant.