Generally speaking mechanical energy is energy which physically moves (the object), while the thermal energy is energy from the movement of atoms. Basically temperature is a measurement of atomic movement (doesn't move object as a whole). Hence heat.
Mechanical energy is a result of kinetic energy plus potential energy of an atom due to the motion of electrons. As the electrons move away from the nucleus, that is to the outer orbitals the potential energy increases, and as the electrons move inward towards the nucleus the kinetic energy increases.
