The OP is in America, so I will assume they are talking about American circulating coins.
American coins - dimes and quarters, specifically - are unusual from a world coin perspective, in that they are made of clad metal - they are a metal sandwich, with a core of pure copper, surrounded by a relatively thick shell of cupronickel (which is an alloy made of 75% copper, 25% nickel. Copper has a lower melting point than cupronickel, so it will melt first.
So if you put a mixed pile of pennies, nickels, dimes and quarters in a box and slowly raise the temperature, here's my understanding of what will happen.
At about 420 degrees C, the zinc cores of the pennies will melt. As the copper plating on pennies is very thin, this will not survive the melting process; the copper will simply dissolve into the molten zinc. At around 900 degrees, the zinc will hit boiling point. At this stage, zinc in open air will start to burn; what happens to your box of coins depends on how airtight it is, and if oxygen can get in and/or zinc vapour get out. When zinc burns it creates zinc oxide, which is white; combined with copper oxides and you'll probably end up covering everything in grey powdery debris.
The next to go will be the copper cores of the dimes and quarters; these will melt at around 1090 degrees C. Note that if the box isn't moving or being jostled about during the heating, the cupronickel shells will still likely hold the partially molten coin together at this stage (kind of like a cheese sandwich full of melted cheese).
At around 1360 degrees C, the cupronickel shells of the dimes and quarters, and the entirety of the nickels (which are made of solid cupronickel alloy), will start to melt. They will completely melt above 1390 degrees C, leaving you a pool of somewhat impure molten copper. If you cool it down and take it out of the box now It will probably look greyish-brown, somewhere between silvery and coppery in colour. Covered in white powder from the zinc, it will probably be greyish in appearance, and not necessarily look like a lump of metal.
Which does leave the question of what kind of donation box is going to be used, that can survive a temperature of 1390 deg C.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis