How does the photoelectric effect coincide with thermionic emission and the particle nature of light? I was watching a video explaining how the photoelectric effect shows the particle like nature of light. my understanding is that the frequency of the light determines the amount of energy delivered to the electron while the intensity (number of photons) determines the number of electrons emited.
If thermionic emission can happen by heating a particle with a laser, it seems to me that higher intensity light is capable of emiting electrons even below the frecquency threshold. Does this mean that the nature of light can be reinterpreted as only wave like?
 A: 
Thermionic emission is the liberation of electrons from an electrode by virtue of its temperature (releasing of energy supplied by heat). This occurs because the thermal energy given to the charge carrier overcomes the work function of the material.


In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface.

You ask:

If thermionic emission can happen by heating a particle with light,

A particle, the electron, cannot be "heated" by light. It can interact with a photon  that composes a light source. If you mean heating a material using lasers and watching the thermionic emission, there exist experiments studying  this, (example) .

it seems to me that higher intensity light is capable of emiting electrons even below the frequency threshold

The photoelectric effect work functions are measured  on cold metal surfaces. A heated solid , by definition of heat , will have a distribution of kinetic energy and for high temperatures of thermionic emission it is the high energy tail of the distributions that will provide enough kinetic energy to overcome the work function of the material studied ( note that the temperature of the material affects the work function ( example).
Light, classical electromagnetic waves, is composed out of a large number of photons, elementary particles in the mainstream standard model.
