The part that will get hot is a SiC fet, probably a TO247 package. The first step is to get the heat out of the package to some metal surface, with low theta and minimal capacitance. That could involve a GaN or BeO insulator. Or we could bolt the fet directly to a very small copper block and water-cool that, with clean water. Or an insulating heat pipe might accomplish the same thing. Since the pulse head will be small, either could also carry the heat away to a big heat sink or radiator.
The three pics in your second link pretty much present the choices. It sounds like the insulating heat pipes get their insulation from a ceramic insulator; I think the heat-transport fluids are conductive.
Are heat pipes reliable? I've heard tales of corrosion and leaks.
When I want is a nice single-crystal isotopically-pure diamond heat sink with fins. I should add diamond to my program.
Diamond conducts heat several times better than copper and its dielectric constant is about half that of AlN or BeO.
I wonder if my customer has cooling water available. That would be nice.