When I think of rectifier designs, high voltage stacks, single phase bridges, and three phase bridges come to mind. These are all made using strings of high voltage, discrete diodes soldered together.

Of all the things to take into consideration when designing rectifiers, "thermal management" is right up near the top of the list.

If you can't get the heat out of the diode, eventually it will fail. At the very least, it will cut the life expectancy of the assembly significantly. By how much? Well, that depends. It's sort of like driving your car when it's low on oil. Sure, you can do it for a while, maybe even a long time. But it increases the wear and tear on the engine. Your engine will fail – sooner or later. Sooner if you didn't keep it well oiled and maintained.

Most of the heat in a diode is dissipated through the leads. Very little heat radiates through the glass body. The thermal conductivity of silver, which is what the leads are made of, is considerably higher than that of borosilicate glass.

There are several ways to get the heat out of a diode.

• First and foremost is to run the diodes well below rated current, voltage, and reverse recovery time. That's wonderful if you have the money and real estate. De-rating means adding more components, which takes up more space, or using components way over the requirements, which usually translate to higher unit costs.
  
• A second approach is to use internal heat sinking. Often thermally conductive heat sinks are added to the leads. This helps spread out the heat, and increase the area over which the heat is dissipated. It increases the thermal footprint of the diode.
  
• Closely related to internal heat sinking is external heat sinking. The assembly can be attached to a base plate made out of copper or aluminum, which is often mounted to an even larger external heat sink. Sometimes the external heat sinks are water, or air cooled.
  
• A third approach is to run the unit in a thermally conductive environment such as dielectric fluid, or SF6 gas. Care much be taken to ensure the volts/mil stress between terminations is not exceeded. A quick calculation can confirm suitability of the fluid or gas.
  

Here is more info on computing thermal impedance of a diode, including a list of thermal impedances for materials commonly used in electrical and electronic industries.