Not a single scientist nor anything in nature has been able to reach a temperature of 0 K or less. As for an upper limit, scientists are not willing to make a guess until more about the universe is known. Some of the highest temperatures in the universe have been found in the cores of stars. Since stars are so far away, it's obvious that we can't just go and stick a huge thermometer in them. So astronomers analyze the light that a star produces.
Spectroscopy is a method that separates a star's light into a bar of several different colors.
Some of the colors are thick and some are thin. The colors will look differently depending on what the star is made of. Once the astronomer figures out what the stars consist of, she can determine how hot the core is. If the star has more of a certain gas than another, then the star will be hotter or colder depending on what that gas is. The temperature at the core is also dependent on how dense the star is.