Be Patient

A classic plaster cast is made of bandage and heated gypsum, a form of calcium sulfate, though a modern cast may contain fiberglass to improve the strength and stability within the cast.

When this dehydrated gypsum reacts with water, the water molecules are absorbed and chemically aligned among the calcium sulfate crystals. This process is an exothermic reaction, meaning giving out heat, as new chemical bonds are created:

$2(CaSO_{4}\cdot \frac{1}{2}H_{2}O) + 3H_{2}O \rightarrow 2(CaSO_{4}\cdot 2H_{2}O) + \triangle$

As a result, while the plaster cast dries up (absorbing water) and hardens into a stronger gypsum form, the patient will feel the warmth gradually coming out of the structure, which will last within 10 minutes.

Moreover, the counterpart of this reaction is called endothermic , literally absorbing in heat, where the chemical bonds are broken into ion forms. An explicit example is when salt is put into the ice water in the bucket, the temperature inside will drop even to the point where it freezes the surrounding. (This is how scientists show how to make juice sherbet sticks to the kids.)

Conversely, this happens because when salt (Sodium chloride) is dissolved in water, its molecules break down into sodium and chloride ions, its core elements, and to do so, they use the energy or heat from the surrounding water molecules, causing the water molecules to be less agile or cooler in the process.

The hydration reaction is an exothermic reaction i.e. heat is released during this process. As a result, the patient should feel warm.

The still unbound water molecules move freely with a specific (translational) kinetic energy determined by the water temperature.

$\frac{1}{2} m_{H_2 O} \cdot \left< {v^2} \right> = \frac{3}{2} k_B T$

with $m_{H_2 O}$ being the mass of a water molecule, $\left< {v^2} \right>$ the mean square velocity of all water molecules, $k_B$ being the Boltzmann constant and $T$ being the temperature.

When, during the hydration reaction, the water molecules attach to the cast , this translational kinetic energy needs to go somewhere. It is converted to rotational and vibrational energy (other degrees of freedom which are strictly speaking also kinetic energy) of the cast which corresponds to an increase in temperature on a macroscopic level.

In other words: By taking the more energetically favorable form of the water bound to the cast, excess energy is freed. It is released in the form of heat and increases the temperature of the plaster.

A more simplistic answer is that the cast will prevent the arm losing any heat naturally to the air, thus feeling warmer regardless of any exothermic reaction.

I only knew the answer as I've had a cast applied before, and can recall the effect of the hydration reaction.

Let’s just remember what happened by understanding that creating a bond release energy while breaking a bond need energy. Let’s say the system is water and the bandage while the surrounding is your hand. So the water is attached to bandage which means inside the system, they create bond and release energy. As a result, the reaction is exothermic and the surrounding (your hand) receive heat and feel warmer

Try guessing sometimes also theres a thing called warm water .... it happens when water gets in contact with warm stuff like skin..... yeah

Spontaneously, things give off heat unless they can absorb it to move to a more disordered state. This is quantified by the difference in Gibbs free energy, $\Delta G = \Delta H -T\Delta S$ , which determines if a reaction occurs spontaneously $\Delta G < 0$ or not $\Delta G > 0$ .

If the water molecules attach themselves to the cast, they become more ordered than when they are flowing around. Because entropy decreases and the reaction still happens, it must give off heat.

Experienced it myself after an accident