The blackening of copper alloys (e.g., basic brass is 33% zinc with 67% copper) is due to the formation of black oxide of copper (the process is known by the trade name Ebonol C: Accordingly, if the copper alloys is containing 65% or more of copper, a black oxide treatment can be applied to alloy surface to blacken by converting the copper to cupric oxide $(\ce{CuO})$. According to Wikipedia, the temperature required to blacken brass alloy is about $\pu{400 ^\circ F} \ (\pu{204 ^\circ C})$.
It is also noteworthy to mentioned here this somewhat cool educational demonstration. According to this Illini website:
[...] penny coins, starting in 1983, were made of zinc with a thin layer of copper plated on the surface. If these coins are heated, the zinc will diffuse into the copper layer, producing a surface alloy of zinc and copper. These alloys are brasses. Not only does the zinc change the properties of copper, but also the color of the brasses changes with zinc content - reaching a golden yellow color at around 20% zinc and golden at 35-40% zinc. Copper also oxidizes when heated in air, producing a black layer of copper oxide $(\ce{CuO})$. Thus when heated, there is a competition between the rate of oxidation (making the surface black) and the rate of diffusion (making the surface a golden-yellow color).
You may use this demonstration to find out the exact temperature when the coin starts blackening (hopefully)!