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Cryogenics is related to very low temperatures, so, what is the term when referring to very high temperatures?

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There is always amplituaestus. Almost meaning "greatest heat" or "A greatness of heat" really hard to do literal translations with Latin – Argus May 22 '12 at 3:29
There is no term, because there is no real field of study here. At high temperatures everything becomes uniform gas. Low temperatures are much more interesting than high temperatures. You should think in terms of $\beta$--- large $\beta$ is a wide open field, and low $\beta$ is just one point. – Ron Maimon May 22 '12 at 3:30

Plasma physics. Sufficiently high temperatures will turn any material into a plasma (decomposing any molecules in the process).

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To give MSalter's answer a "ics" word you say "magnetohydrodynamics".

However, I don't think the parallel is perfect. One can say that you have a cryogenic gas system or a where you simply mean "very cold" or cyrogenic hydrogen target (if you're a particle physicist, say) where you mean "cold enough to be liquid", but there doesn't seem to be latin word for "very hot": we have "high temperature ceramics".

"Thermogenic" would seem to be the obvious parallel construction, but it's taken.

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I would say simply "high temperature physics", just as the Kurchatov's institute for High Temperatures (litteral translation) in Russia.

I would be careful with the "magnetohydrodynamics" term used by dmckee, as this term covers a discipline in which conductive fluids move while undergoeing electro magnetic forces. You can do magnetohydrodynamics (MHD for intimates) with just very salty water, two blades, a 9 V battery and a Neodymium (NdFeB) magnet, at home: put the magnet under a dish filled with salty water, connect the battery to both blades (+, -), and put the blades inside the water, face to face, above the magnet: if your magnet's field reaches the inside of the dish, you should see the water move. This is simply Lorentz force acting on a conductive, liquid medium. Very funny to do. But has nothing to do, at least not in all cases, with high temperature physics: MHD can be used with plasmas and hence high temperature physics, but plasmas are not necessary to observe MHD, as well as a magnetic field (without which there would be no Magneto-hydro-dynamics) is not necessary to have interesting applications with high temperature physics, and plasmas.

Finally, note that high temperature physics is not automatically related to "gaseous" plasmas: the center of the earth, the center of white dwarfs (the stars), are very "hot" media, but are not really comparable to a free, gaseous plasma. This field is more related to the "warm dense matter" (as are some nuclear experiments), an active subject of research nowadays.

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