For temperature there is a definite and incontrovertible lower limit: 0 K. Among the closest things to absolute zero in the universe is the temperature of supermassive black holes (10-18 K). At this temperature it will take them 10100 years and more to evaporate their mass. Yes, that’s a one with one-hundred zeros. If the universe really does keep on expanding as believed by most scientist today, supermassive black holes will be the last remaining objects in the fading universe. Compared to their temperature, the lowest temperature ever achieved in a laboratory (10-12 K) is a true hellfire, despite it being many orders of magnitudes lower than the background temperature of the universe (2.73 K and slowly decreasing).
In terms of temperature, helium is an exceptional element. The fact that we almost always find it in the gaseous state is a result of its low boiling point (4.22 K). Even on Uranus (53 K), since the downgrading of Pluto the coldest planet in the solar system and by far the planet with the most inappropriate name, it would appear as a gas. Another temperature you definitely should remember is 92 K. Why? Because at this temperature the material Y-Ba-Cu-oxide becomes superconductive and there is no material known to man that is superconductive at higher temperatures. Note that you want a superconductor to do what it does best at temperatures as close to room temperature as possible because otherwise making use of this effect will require enormous amounts of energy for cooling.
The lowest officially recorded air temperature on Earth is 184 K ≈ -89 °C, so measured in 1983 in Stántsiya Vostók, Antarctica. Just recently scientists reported seeing an even lower temperature, but at the time of writing this is still unconfirmed. The next two values are very familiar to you: the melting point (273 K ≈ 0 °C) and the boiling point (373 K ≈ 100 °C) of water. But I would not advise you to become too familiar with burning wood (1170 K ≈ 900 °C) or the surface of our Sun (5780 K ≈ 5500 °C).
Temperatures in a lightning channel can go far beyond that, up to about 28,000 K. This was topped on August 6, 1945, when the atomic bomb “Little Boy” was dropped on Hiroshima. It is estimated that at a distance of 17 meters from the center of the blast the temperature rose to 300,000 K. Later and more powerful models of the atomic bomb even went past the temperature of the solar wind (800,000 K).
If you are disappointed about the relatively low surface temperature of the sun, keep in mind that this is the coldest part of the sun. In the corona surrounding it, temperatures can reach 10 million K, the center of the Sun is estimated to be at 16 million K and solar flares can be as hot as 100 million K. Surprisingly, mankind managed to top that. The plasma in the experimental Tokamak Fusion Test Reactor was recorded at mind-blowing 530 million K. Except for supernova explosions (10 billion K) and infant neutron stars (1 trillion K), there’s not much beyond that.