Depending on the pan it can be a disaster or mostly fine.
The main factors are the heat conduction, thermal expansion and flexibility of the material.
When you expose something to a temperature change that change takes time to travel through the material. During that time different parts of the material are at different temperatures and the worse the heat conduction (the better it insulates) the bigger that temperature difference gets.
When materials change temperature they change size too. Some materials are more affected by this than others.
If you have a material that has been heated to different temperatures and different parts have changed size differently it puts stress on the material. If the material is flexible it just bends a bit, if it’s rigid it shatters.
So glass dishes are the worst, at least untempered glass. Many fancy pans are made of 2 materials (like a copper core with a steel or aluminum coating. Those layers can separate or cause warping. A solid metal pan might warp a little but it’s pretty robust to temperature shocks.
My wok is basically immune to such problems. It’s a thin piece of high-carbon steel. Heat travels through super fast. It’s standard practice to clean woks by dumping in some cold water and scrubbing with steel wool.
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