In physics, heat is based on energy and that energy can be measured objectively. However, physics allows for several different ways to measure heat including radiant heat (actually, infra-red radiation) or an object's temperature (actually, molecular motion, often vibration). There is even a way to define heat according to the population of electron orbitals above a "base" state.
However, "heat" can also mean the sensation of heat, which is subjective. English allows us to have confusion like that. If you carefully qualify your question, you would find that both facets of the word "heat" have meaning, each in their own contexts.