The work is dedicated to the development of the electron-lattice energy exchange theory in metal particles, including dependence on particle size and electron temperature. We compared, for infinite metal, the expressions for the constants of the electron-lattice energy exchange by using the quantum-kinetic approach, with the classical kinetic approach. Both methods give the same result. But as we show, a quantum-kinetic approach in its standard form, for the metal particles smaller than the mean free path of electrons, cannot be applied, while the classical approach can be easily adjusted for such particle. We found a new peculiarity of the electron-lattice energy exchange. This exchange essentially depends on temperature if a particle size is in the range near a certain "magic size". The change of the electron temperature can alter (around the "magic size") the number of the acoustic modes, which are involved in energy transfer. As a result, the constant of the electron-phonon interaction in nanoparticles can be either much higher or much lower than the corresponding constant for infinite metal.