russ_watters said:
You don't need to know temperature, you need to know heat. Temperature is not heat: Your description is incomplete at best and is not enough to help answer your main question (how to power it).
The filament of a AAA battery powered flashlight gets much hotter than 500F, for example, but I doubt that that will satisfy your needs.
More to the point, there is a vast difference between the energy/heat absorbed and released by a cigarette lighter and a coil burner. If the cigarette lighter meets your needs, then the power requirement is around an order of magnitude lower than you seem to think it is.
So: What matters isn't the temperature, but how fast you remove heat from the burner. Do you know how fast you are removing heat from the burner? How big of a cylinder? Is it filled only with air? Is it oriented vertically? Is it insulated? How hot do you want the object to get? How fast? From what starting temperature? What is the specific heat capacity of the object?
We cannot help you unless you can help us figure out (or just tell us) how fast you need to produce heat.
I lack knowledge when it comes to this but hopefully this answer will give you a better idea.
Lets use the coffee mug example: http://i00.i.aliimg.com/photo/v0/379750484/16_oz_metal_mug_with_handle_office.jpg
That is a very similar shape and size to what the product looks like from the outside.
Put maybe 8 tiny holes the size of the plastic part of a thumb tack on the sides. It is made only of thin metal. No other insulation. Nothing else inside it besides the parts necessary to make the heating element work. The cylinder stands vertically. The top is closed. The bottom is open but the object that I am trying to heat using the heating element attaches to it, so the only ventilation will really be those holes made.
The heating element will be about an inch away from it. The product will usually be used outdoors. So the temperature of the environment before using it will be around 30-100F, with 0F and 110F being fairly extreme outliers.
The object I am trying to heat holds heat very well as it is usually ceramic. The temperature it needs to reach is somewhere between 210-250F. Without absolutely disclosing my idea for the internet I am trying to replicate what happens to it when you put coals very near it or on top of it.
Now let's say there is hole that goes through my product in which air will move through. When air moves through the coal is causes it to rise in temperature temporarily, which I also need it to do. Thus why I was asking about having some sort of flow sensor that would cause my heating element to increase in temperature when it detects air flow.
The amount of time needed to heat this object does not have to be very precise. If necessary it can take up to 5 minutes. Keep in mind I want the heating element to continue staying on so if the temperature of my object changes maybe 20-30 degrees higher within an hour due to prolong heat, that is actually desired since it replicates what the coals would do. I want this heating elements battery to last as long as possible. If it can last 2 hours, cool. If it can last 10 hours, AWESOME.