Depends on how you define "black" since WIMP heating, according to Adams & Laughlin's estimates, will heat a white dwarf to 63 K, making it still glowing in IR. But if we're talking below the temperature at which an object glows with its own heat, roughly 800 K, then a white dwarf that's presently at ~4000 K will take about ~2 trillion or so years to cool to that point. An isothermal ball would cool quicker (just ~1 trillion years), but real white dwarfs have an opaque outer crust which slows down the escape of heat.