For example 1:

Let's say that the balls are made of gold. Gold is very dense, so there will be plenty of kinetic energy, and only a small portion will be lost through air resistance.

Some significant physical properties:

(

https://en.wikipedia.org/wiki/Gold) Density: 19.30 g/cm3

(

http://www2.ucdsb.on.ca/tiss/stretton/database/Specific_Heat_Capacity_Table.html) Specific Heat Capacity: 0.129 J/gK

Let's say a ball in a certain newtons cradle made of gold weighs about 100 grams. The strings are 15 cm long. This is larger than your normal newtons cradle, btw. Now we can have a few different scenarios, each including raising two of the balls on opposite sides up so that the string is horizontal. At this point the balls are 15 cm high from the lowest point they can reach, so their potential energy (which is then all converted into kinetic energy) is E

_{p} = m*H *g. E

_{p} = 0.1 kg * 0.15 m * 9.83 m/s

^{2} (at poles, where gravity is strongest for greatest potential energy) = 0.14745 J (No rounding).

First scenario, optimal one: Cradle consists of two balls only. When we drop the balls and they collide, their kinetic energy is turned into heat. We can calculate how much they heat up using the formula E

_{heat} = m*c*T, where c is specific heat capacity and T is temperature. We can write this formula as T = E

_{heat}/(m*c)

Since there is only two balls, each ball absorbs their own kinetic energy into heat. So each ball will heat up by T = 0.14745 J / (100 g * 0.129 J/gK) = 0.01143 K (or °C) (Rounded). The balls will get 0.01143 °C hotter.

I don't think we need to do the other scenarios, as they will get lower values (more balls, so a normal cradle. That's more mass, so the energy will spread more and heat up less). Some of this energy turns into sound as well (so you can't see this blabla energy, but you can actually hear it). And no, the contact areas won't be a lot hotter. Each individual atom in the balls carry their own kinetic energy, and turns it into heat energy which only themselves and their neighbors absorb. So the heat is spread out evenly. I think you are misjudging the amount of energy this experiment works with.