In the following passage, I use “heat” in its most narrow, physically precise manner: as a verb only. This is consistent with the way the science of heat - thermodynamics - views the concept.
When you heat an object, this may cause the temperature to rise. This is because the internal energy of the object has increased. This internal energy is the sum of the random kinetic and potential energies of the particles making up that object. When there is a temperature rise, the internal energy increases because the particles move faster (their kinetic energy increases) - that is they go from point to point (translate) or rotate or vibrate more.
In a solid the main mode of movement is vibration, while in a liquid the particles are free to also rotate while in a gas all three modes are undertaken but the main driver of the temperature rise is due to an increase in the translational motion of the particles. There is one other way to increase the internal energy of an object through heating and this does not cause a temperature rise. How is it we could heat something and yet not cause a temperature rise? This can be so if the internal energy rises but does not cause a change in the kinetic energy of the particles and this is possible if the heating causes only the potential energy of the particles to change. And what this means for an object is that the potential energy in the bonds changes. The bonds might be between atoms (intramolecular) or between molecules (intermolecular).
During a change of state this is precisely what happens.
The bonds are broken (or created) and this takes energy to do - but the kinetic energy of the molecules does not change and so the temperature does not rise.
To be clear: during a change of state heating causes no change in temperature. Consider one such change of state (say solid ice at 273K (i.e: 0 degrees celcius)) to liquid water at exactly the same temperature of 273K - the temperature does not change despite the material being heated. This is because when you heat the object the internal energy increases not because the particles are moving faster but rather because the potential energy in the bonds changes. Thermal energy is used to break the bonds between the particles. In the case of water, the strong hydrogen bonds require a large amount of energy to be overcome and this is one reason the specific heat capacity of water is so high.
What I say above is taken largely from the works of the great physical chemist, Peter Atkins. In his book "A brief introduction to Thermodynamics" he writes “In thermodynamics, heat is not an entity or even a form of energy. Heat is a mode of transfer of energy. It is not a form of energy or a fluid of some kind or anything of any kind. Heat is the transfer of energy by virtue of a temperature difference. Heat is the name of a process not the name of an entity.”