Pulsars are rapidly spinning, strongly magnetized neutron stars. Their electromagnetic dipole radiation is usually assumed to be at the expense of the rotational energy. In this work, we consider a new channel through which rotational energy could be radiated away directly via neutrinos. With this new energy conversion channel, we can improve the chemical heating mechanism that originates in the deviation from beta equilibrium due to spin-down compression. The improved chemical and thermal evolution equations with different magnetic field strengths are solved numerically. The results show that the new energy conversion channel could raise the surface temperature of neutron stars, especially for weak field stars at later stages of their evolution. Moreover, our results indicate that the new energy conversion channel induced by the non-equilibrium reaction processes should be taken into account in the study of thermal evolution.