Actually, this is a hard problem, if you want an accurate solution. The power dissipation needs to be perhaps a Watt or so and, from experience of burned fingers, I'd say that would need around 5A but the temperature reached would depend a lot on the surroundings and heat loss.
I think the best solution would be to use AC, from a very few turns of thick wire on a transformer with only a few volts on its primary - i.e. you may need two step down transformers if the turns per volt on your mains transformer are too high - making the voltage steps too coarse. You would need a really thick conductor, bonded very well to your wire or the contact resistance will dominate.
Hang on , Is this just a foam cutter that you're planning to make? The nichrome wire from a broken toaster in a skip would cost nothing.