Temperature. Temperature is the physical property of a system which underlies the common notions of "hot" and "cold"; the material with the higher temperature is said to be hotter. Physically, temperature is a measure related to the average kinetic energy of the particles in a substance.
If the temperature of an object is simply a measurement of the average kinetic energy of the molecules within it; is it possible to convert the temperature of an object, given it's volume, into either a value for the average speed of movement of each molecule or the average kinetic energy of each molecule?
Thee is no need to convert the kinetic energy to beam temperature. The beam energy is deposited in the near surface of the ingot. A small volume of the ingot is heated enough to vaporize the material.
If you consider that friction generates thermal energy, theoretically this is possible. You need some form of thermal machine that is able to convert this low delta temperature heat into some form of better energy, for instance electric energy, that in turn moves a motor that generates the kinetic energy mentioned by your question.
We can easily show the conversion of kinetic energy to potential energy, and vice versa. However, conversion of these types of energy to internal energy is more challenging to demonstrate. We do not have everyday experience with falling objects raising their temperature and the temperature of the pad after the object landing.
Thinking about temperature and heat in terms of energy is very useful and helps us understand many of the things that happen around us. Nevertheless, this is not the only thing we will talk about. Since this is a temperature conversion tool, it is only fair that we talk about units of temperature. We also need to acknowledge the different ways ...
As you say, kinetic energy of large objects can be converted into this thermal energy. For example, if you drop a water balloon onto the ground, its kinetic energy is converted mostly to thermal energy. If the balloon weighs 1 kilogram and you drop it from about 2 meters, it will heat up by less than .005 degrees Celsius.
The energy can be converted to in different forms, however, its total energy is not changed. The common energy forms include the radiant energy, kinetic energy and various types of potential energy. It is a scalar. The SI unit of energy is joules, symbol "J". but in some areas are accustomed to use other units, such as kilowatt-time and calories.
Thermal energy tends to increase the volume / size of a material. Look at the steam engine. The way how you extract mechanical energy (potential and kinetic) from steam engine is by the preassure that steam in the chamber creates.