I feel like this deserves more attention.
The heat capacity of water is 4 J/g/K, so if we assume that our insulated container cools by about 1K every 400s, we need an energy input of 10^-2 J/g/s.
If we take the obvious approach of using half anti-water to make our coffee (containment and modulation of the annihilation is left as an exercise for the reader), and noting recent expert commentary that we can probably get 92% efficiency…
Nuclear fission / fusion? - #45 by Pasta
…we have 8 x 10^13 J/g available.
So we can keep our coffee warm for 8 x 10^15 s, or 250 million years as a rough approximation. Of course, the volume of coffee would steadily decrease, which is a drawback to this method.