First: please don't talk about heat "accumulating". Heat is energy in transit from a region of higher temperature to a region of lower temperature. If you are considering a defined region, then the energy residing in that region is classed as internal energy.
Evaporation is, as I said in my last post, the unco-ordinated escape of molecules from the exposed surface of a liquid. At any instant, molecules in the liquid will have different kinetic energies. Their mean kinetic energy is usually roughly proportional to the Kelvin temperature. Most of the molecules in the liquid won't have enough energy to escape from the liquid surface, against the (shortish-range) attractive forces from other molecules in the liquid surface. But some molecules (in a short time interval) will have experienced a succession of 'lucky' hits from other molecules, and so will have acquired energies well above the mean. Even enough energy for them to escape (if they are in the surface)! This is evaporation!