What temperature can I reach using magnifying glass at night? What about full moon night and what about the night without moon?
Let's say in both cases we have no clouds and +25C air.
How big should the glass be to burn the paper? ant?
 A: According to some forum thread the one needs ~70mW to light a match. And according to the answer given in related question (found by John Rennie) the full moon gives $0.1mW$ using solar cell and mirror with $1m^2$ surface area. I'm not sure why he took solar cell, but his mirror seems to result in 30m in diameter.
There in comments thread some J... guy says the equivalent to 25mm diameter lens in daytime is 17m in diameter lens under moonlight. 25mm lens under sun seems for me to be enough big to burn anything that people use to burn, so lets say for lighting the match we would need 10m lens at night.
But what I've just realised is that the Moon is about 30' in angular diameter and corresponding tangent is around 0.009, that means from the 5 meters distance (average distance from the reflector surface to the match) the projected moon image would be around 50mm in diameter, that is ~200 weaker than if it fully concentrated on the match head. To compensate that we need to take 15 times larger reflector (150m in diameter) but the mirrored beam would also become 15 times longer, that means... no matter how large reflector we take, we'll get only 0.5% of power needed to light the match using light directly. That's probably why the one took solar cell.
But this still does not answer my exact question -- what temperature I can get?
