Rapid heating or cooling can create temperature gradients inside a solid. Different regions then try to expand or contract by different amounts, producing thermal stress even without an external mechanical load.

A rough constrained-stress scale is

$$\sigma_{th}\sim E\alpha\Delta T,$$

modified by geometry and Poisson effects. Large elastic modulus $E$, thermal-expansion coefficient $\alpha$ and temperature difference $\Delta T$ therefore increase the potential stress.

The temperature gradient itself depends on heat transport. A material with high thermal conductivity tends to equalize temperature rapidly and reduce internal gradients; a thick body or rapid surface temperature change tends to increase them.

Brittle materials are especially vulnerable because cracks can propagate before plastic flow substantially relaxes the thermal stress. Thermal-shock resistance therefore combines thermal and mechanical properties rather than depending on one scalar property alone.

A qualitative material-design preference for many brittle applications is:

• low thermal expansion;
• sufficiently high thermal conductivity;
• high fracture resistance;
• geometry that avoids sharp gradients and stress concentrations.

Preheating, controlled cooling, thinner sections and graded interfaces can also reduce thermal shock. The key mechanism is the coupling

$$\text{temperature gradient}\rightarrow\text{incompatible thermal strain}\rightarrow\text{stress}\rightarrow\text{possible crack growth}.$$