Former temperature metrologist here.
As noted by a couple others, there are two defined temperatures:
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Absolute Zero (defined as 0 K)
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The triple point of VSMOW water (defined as 273.16 K = 0.01 °C)
Again, these are defined; they will never change. All other temperatures are based on these two standards.
Interesting tidbit of info: it is impossible to measure the temperature of the triple of water. It is defined, remember? You can’t measure something that’s defined. It is used to measure the temperature other things.
The triple point of VSMOW water is pretty easy to achieve in an analytical lab. All you need is a water triple point cell (around $1000) and some dry ice. After forming the mantle, it will be at 0.01 °C for two or three hours, and then it will melt. (Well, not quite. A practical water triple point is not exactly 0.01 °C. You need to use correction factors.) During that time, you can stick any thermometer into the well for calibration. Once it melts, you simply have to reform the mantle.
But also as noted by others, there are other fixed point temperatures that can be used for calibration. These include the triple point of mercury (−38.8344 °C), the melting point of gallium (29.7646 °C), and the freezing point of indium (156.5985 °C). But these are not defined temperatures; they are simply known out to around ± 0.00003 °C or so. In the future they could change. As an example, we might later discover the freezing point of indium is closer to 156.5984 °C than 156.5985 °C. Or the freezing point of silver is closer to 961.79 °C instead of 961.78 °C. But absolute zero and the triple point of VSMOW water will never change. They’re (Again!) defined, and are used as a basis for determining the temperature of all other things.
So… how does NIST know what the temperature is for the triple point of mercury? Or the freezing point of zinc? Or the freezing point of indium? They use gas thermometers. You can’t buy these; they are very special, very difficult to use, and very expensive. Physicists like them because they’re based on physical laws. They first taking a reading w/ a gas thermometer in the triple point of water, and then they use it to measure the temperatures of the other fixed points.
Note that the melting point of water and the boiling point of water are no longer considered fixed points. And because of that, it is technically incorrect to say the melting point of water is exactly 0 °C, or the boiling point of water is exactly 100 °C. The latest measurements suggest the melting point of VSMOW water is around 0.000089 °C. So it’s good enough for many applications, but temperature metrologists still don’t like it.
So after NIST measures the temperature of all of its fixed points using fancy gas thermometers, all the fixed points (including the triple point of water) are available for calibrating practical standard thermometers. The most common being standard platinum resistance thermometers (SPRTs) and type S thermocouples.
Thousands of calibration labs across the world use an SPRT and type S thermocouple as their standard interpolation instruments for temperature calibrations. (Most also have a triple point of water cell. The cell is necessary when using an SPRT, as you must first stick the SPRT in the cell to show the SPRT what 0.01 °C looks like, and then you use it to calibrate other sensors in a temperature controlled bath.) At these labs, they use the SPRT and type S thermocouple to calibrate a wide variety of temperature sensors and readouts using a comparison method. These labs will periodically send their SPRTs and type S thermocouples to NIST (or another qualified lab) for calibration. We had to send our SPRT back to NIST whenever its resistance at the triple point of water drifted by more than 0.001 Ω.