Two types of temperature controlled soldering irons are available. One type is plugged in and can heat up on its own with no temperature control whatsoever; the other has a variable temperature dial that regulates the temperature at the tip. They will each do the job, but the regulated ones can be temperature controlled for more precise and intricate soldering tasks.
The Wattage Factor
Most people might think that the higher the wattage of a soldering iron, the hotter it will get. The truth is that a higher wattage soldering iron will be able to more precisely keep the iron tip at exactly the same temperature. This is especially helpful when soldering multiple joints in succession, like circuit board work or soldering larger joints which take a longer time to heat up. For those applications, more wattage means a more stable temperature at the tip and also at the soldering joint.
Temperature in General
Lead-based solder should be soldered with a tip temperature of between 600 and 700 degrees while lead-free or silver solder should be soldered between 700 and 800 degrees. Higher temperatures may make them melt faster, but you stand a risk of atomizing the solder which will compromise the electrical connection. It's better to solder at a lower temperature to make sure that the connection will be electrically active when finished.