Hehe, I built a similar machine last summer with a friend. We had around 500+ 3"x3" mirrors mounted on a 6'x6' wooden plate. The focal lenght was ~5ft and the focal point about 6 inches wide (we had so much mirrors that we didn't took the time to align every single one of them perfectly). It took us a few weekends (and a lot of beer) to build this monster.
We calculated that a black body should reach a theoretical temperature of 1400C at the focal point but I don't know if we actually reached that. Wood ignited instantly and cell phones melted in a few seconds, but we could not get aluminium to melt completly (probably because it has such a poor emissivity). The first thing we burned was an empty box of Sunlight Soap ... it actually took us a few hours to realise the irony of the situation.
I know this is shameless ranting but I'm kind of proud of this thing.
(I have a few picture but I don't have enough posts yet to upload them
)
Anyway, if you want to calculate a theoretical temperature of an object at the focal point you can use Stefen-Boltzmann law. If you want to maximize its efficiency find some black paint with a very high emissivity.
