People often want to have variable temperatures for decorative soldering.
It is often recommended to use a rheostat in circumstances where the soldering iron does not have an internal temperature control. The rheostat reduces the current reaching the iron. The degree to which you have to do this is related to the speed or amount of work you are doing with the iron. With reduced current, the iron can not build up to its previous temperature so quickly. Therefore, it is a matter of individual practice on the rheostat setting you use.
Temperature controlled soldering irons attempt to maintain a set temperature. This is controlled by the combination of the microchip in the iron and the tip. So to adjust your temperature all you need is a few different tips. For example, a number 7 tip lets your iron heat to 700F degrees. For decorative soldering your need tips of lower temperatures, usually a number 6 or 600F degree is enough of a reduction for most decorative stuff. A number 8 tip (800F) will let you work at a higher temperature if you work quickly.
You can buy an iron (not temperature controlled) and a rheostat but buying tips for the temperature controlled iron is cheaper. A rheostat is NOT a temperature controller. A rheostat actually reduces the power supplied to the iron, thereby making it take longer to heat or re-heat after a period of soldering. Many people advise that using a temperature controlled iron with a rheostat can damage the thermostat. Using an iron without a rheostat, provided you work relatively quickly, you will probably be able to solder all the joints in a small or medium panel without stopping to let the iron 'catch up'. In this case the temperature is controlled by the heating power of the iron balanced by the cooling effect of making the soldered joints.
With a temperature-controlled iron, if it is left idle, it will quickly reach its maximum operating temperature - just as quickly as an uncontrolled iron of the same power. When you start soldering, the cooling effect will trigger the temperature controller to provide full power until the operating temperature is reached again. Using an iron with a rheostat, you will need to slow down a little if you are to do that same panel without stopping to let the iron re-heat. In this case the temperature of the iron is controlled by the (reduced) heating power of the iron balanced by the same cooling effect of making the soldered joints.
Without a rheostat, if an iron is left idle, it will eventually reach its maximum temperature. This is usually too hot for soldering lead, but OK for joining other metals. With a rheostat, if an iron is left idle with the rheostat set to (say) '6', it will still reach its maximum temperature but very much slower than the one without a rheostat.The big advantage of the temperature-controlled iron is that you know it will never get too hot for the work you are doing, and that it truly provides that 100 watts (or whatever) power to keep it hot even when you are soldering at top speed.