Are there specific methods to brewing the perfect Turkish coffee and temperature to heat it to?
You should heat your coffee upto about 70 degrees Celcius so it builds a foam or froth but do not let it boil! You need to keep it at this stage for as long as you can, and if the coffee starts to get to hot and appears to rise then move it off the heat and repeat at most 2 times.
A few important things are
- use fresh coffee or it will not foam as well
- pre-heat the water in the pot first, without the coffee, just until it starts to heat up
- do not stir until the coffee sinks itself
- allow the coffee to heat slowly, not on a high heat (I don't directly place the pot on the heat ring - slightly off of it)
Here's a link to a useful page on Turkish coffee world website with a method for making Turkish coffee. http://www.turkishcoffeeworld.com/How-to-make-Turkish-Coffee-s/54.htm
I would like to excuse and interrupt this thread kindly as an experienced native drinker.
The supplied link in @William Moore's answer requires sugar. The continuous misunderstanding about sugar usage with Turkish brewing in North America is so surprising to me. In Turkey, regular Turkish coffee drinkers hardly –if not never‒ drink their coffee with sugar. However, sugar is optional in recipes.
In @William Moore's own recipe, in 2nd article, pre-heating does not add any visible advantage, only shortens the time to brew. This is actually what is needed to keep the foam intact and prevent the vaporization of the lipids in Turkish brewing. However, you can provide it by using stronger fire easily in contrast to William Moore's 4th article. It is better to use the time span as the size of your cezve may change, you may brew just for yourself or for five people.
The recipes mentioned here has flaws in my opinion and I don't think you can brew delicious Turkish coffee based on these.
Please check this answer. I have explained my own style of brewing Turkish coffee with photos. Also, commented a more detailed recipe that includes quantitative values of an official Turkish Coffee Institute.