How are transistors on processor chips designed to withstand high operating temperatures?
The size of a transistor has nothing to do with how able it is to withstand high temperatures. The temperature has a more or less similar effect on all devices, large and small.
At high temperatures there is more stress on the devices and that mostly results in higher leakage currents (current flow when the device is off and ideally no current should flow) and potential damage to devices and the connections between devices.
One important effect at high temperatures is Electromigration which is an effect that can damage the connections (metal tracks) in a chip and that can eventually break the chip making it unusable. Electromigration is very temperature dependent so chip designs must be made such that this effect is not an issue even if a chip operates at high temperatures (for example 90 degrees C) over its lifetime (for example 10 years of continuous operation).
From your question it appears that you think that operating temperatures are increasing. Well, they're not. Depending on the manufacturer the maximum operating temperature is usually around 90 C to 100 C. Modern CPUs monitor their own temperature and slow down (throttle down) when they get too hot. That means they do not allow themselves to get hotter than 90 C or 100 C.
If a manufacturer would choose to increase that maximum operating temperature to for example 120 C then that will impact the lifetime of the chip. If you used such a chip like most users do then probably it will last you a lifetime.
But if you use that same CPU for mining cryptocurrency so it operates at 120 C continuously then its lifetime might be shortened significantly. Maybe it breaks after a few months. You could then complain to the manufacturer that the chip was faulty. So the chip manufacturer limits the operating temperature to such a value that they can guarantee a long lifetime (say 10 years) of continuous operation at that temperature.
If you want a more in-depth understanding of the deterioration of semiconductors (chips) due to high temperature then you will need to study semiconductors and PN junctions. It is complicated material and not something that can be explained here or even in &quot;layman's terms&quot;.