I know that if you have the right kind of device you are supposed to roast them over the open flame in the fire. Unfortunately I don't have one of those, so I'm curious if I can throw them in a pan, set them on top of my wood burning stove and just stir them every once and a while. If so, can anyone suggest how hot I should get my stove and how long I should cook them?
Chestnuts can be rosted in the oven, no special equipment necessary.
You should prepare them properly, though. First, soak them in lukewarm water for at least 30 minutes. This will soften the skin and help to loosen the fuzzy inner skin later. Then, use a small knife to cut either a slit or a cross on the round side. Place them, cut side up, on a baking tray and roast at 180-200 °C / 350-400 °F for about half an hour. The cuts should open when the chestnuts are done.
If you want to try this on your stove, prepare them the same way, then roast in the pan. Aim for a rather hot stove, mimicking the coal fire, stir them often. If possible, use a cast iron pan rather than non-stick, as the coating might suffer.
Some street vendors here add a dash of water to the roasting pan (over the coal fire) to create steam once in a while. As to time: see above, cuts should open and chestnuts can be easily pierced with a knife.
Did you know than you can also boil chestnuts? Prepare as described above, then boil for about 10 minutes.
Where I live, chestnut sellers in the streets roast them in pans over hot coals. I just do them in the oven at about 180C. Give them about 20 minutes and then stick a sharp knife in one of them.
Note that you might also want to prick them with a sharp knife before cooking, to avoid (or at least control) explosions. If you hear popping sounds, they're getting hot enough to produce some steam, although that doesn't necessarily mean they're cooked through.