Your best bet is to pour the coffee out of the press into a thermos right after brewing. Even after you push down the filter screen, the coffee is still in contact with the grounds at the bottom and will continue to extract. Eventually, it may get bitter. Pouring it into an insulated thermos will keep it hot for quite some time and will prevent any bitterness.
Of course, the solution in our office is just to drink it faster ;-)
Alex
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