As the universe expanded and cooled after the Big Bang, the heat energy present in the early universe was indeed dispersed. The concept of "heat" refers to the transfer of thermal energy from one object to another due to a difference in temperature. In the case of the early universe, the heat energy was spread out as the universe expanded, leading to a decrease in its temperature.
During the early stages of the universe, it was in a state of extremely high temperature and density. It was filled with a hot, dense plasma of particles, including photons (particles of light) and various elementary particles. As the universe expanded, the photons and particles within it spread out, leading to a decrease in their density and, therefore, a decrease in the temperature of the universe.
The cooling of the universe is primarily attributed to a process called cosmic expansion or cosmic redshift. As space itself expands, the wavelengths of photons traveling through space also stretch or "redshift." This stretching of the photons' wavelengths corresponds to a decrease in their energy and an overall decrease in the temperature of the universe.
It's important to note that the cooling of the universe is not analogous to heat transfer in the usual sense, where heat is transferred from a hot object to a cooler one. Instead, the cooling of the universe is a consequence of the expansion of space and the stretching of the wavelengths of photons as the universe grows larger.
In summary, the heat energy in the early universe was dispersed as the universe expanded, leading to a decrease in temperature. The cooling of the universe occurred as a result of cosmic expansion and the stretching of photons' wavelengths, rather than the transfer of heat to something else.