How Is It Possible To Measure Extreme Temperatures? (>2 Billion Kelvin) Linked Article: Record Set for Hottest Temperature on Earth: 3.6 Billion Degrees in Lab

Scientists have produced superheated gas exceeding temperatures of 2 billion degrees Kelvin, or 3.6 billion degrees Fahrenheit.
This is hotter than the interior of our Sun, which is about 15 million degrees Kelvin, and also hotter than any previous temperature ever achieved on Earth, they say.

I don't see how is it possible that these scientists manage to measure two billion Kelvin. Are there such measuring instruments that can measure extremely hot stuff without melting and still get a proper reading, or is it a theoretical deduction?
 A: Fusion is plasma physics, and in plasma physics the temperature is defined by the average kinetic energy of the ions and electrons in the plasma.
Therefore the kinetic energy distributions  have to be measured and they have developed ingenious methods of doing so. Fitting with the black body radiations  curves allows an estimate of the temperature.
There are more ingenious methods developed, using Thomson scattering, which allow by scattering light  on different ions accurate measurements of temperature.
Very high temperatures can be measured for the stars from their black body radiation and the spectral distribution of the light reaching us also.
A: One method mention by Anna V is to use X-ray Thomson Scattering, which is also known as Compton scattering. I figured I would expand on how this works.
When x-rays scatter off of stationary free electrons, relativistic energy and momentum conservation requires that the scattered photon is shifted to lower energy (longer wavelength). The shift is known as the Compton shift, and is given by $\Delta E = \hbar^2 q^2 / 2m$ where $q$ is the momentum transferred to the electron (which can be determined from the scattering angle).
However, the electrons in any material, and in particular an extremely hot, dense plasma, are not stationary. Instead they have some momentum distribution, which is determined by the electronic wavefunctions (property of the material) and by the temperature. Scattering off of a moving electron gives (again by energy and momentum conservation) $\Delta E = \hbar^2 q^2 / 2m + \hbar \vec{q} \cdot \vec{p}/m$, where $\vec{p}$ is the momentum of the electron before scattering.
This Doppler effect causes, for a constant incident x-ray energy, a broad down-shifted peak to be present in the scattered x-ray spectrum. The center is at the standard Compton shift, while the shape of the peak can be used to extract the electronic momentum distribution. From that it is possible to extract a temperature.
A: To measure such temperatures, one can observe and analyze the radiation of the "hot stuff", as the spectrum and intensity of such radiation depends on the temperature.
