This is a common misconception regarding heat. Heat is the transfer of thermal energy down a temperature gradient. Thermal energy (or internal energy) is the sum total of the kinetic energy and potential energy of the molecules in a system. The kinetic energy includes translational, rotational and vibrational energy levels. The potential energy is associated with the vibrational and electric energy of atoms within molecules (this includes energy stored in the chemical bonds). If the substance is a conducting metal, the internal energy also includes the energy possessed by valance electrons.
Note the differences between heat and thermal energy.