Most gemstones can melt, although doing this can change their chemical compounds. Depending on how hot a gem gets, it can turn to powder, so you have to be careful.
Typically, you should be able to heat a gemstone if you want to enhance its natural color and shine. Doing this is very common and shouldn't be too hard to accomplish, but not all gemstones can withstand extreme temperatures.
Usually, it's best to keep a gemstone under 2,000 degrees Fahrenheit during the heating process, or you risk damaging or melting it. According to Earth's Treasury, a Montana sapphire can withstand up to 3,711 degrees before it melts, while a rutile gemstone has a melting point of only 1,843 degrees Fahrenheit.
When it comes to why you would heat a gemstone, this essentially enhances its natural color and improves the overall look of your gem. Heat can be used to lighten and darken gemstones, usually making them appear more vivid.
An unheated gemstone is essentially a gem that a human hasn't thermally modified. Unheated gemstones tend to have more value than heated options but are harder to find.