Pardon me while I try to construct the right hypothetical:
I was invited to a state dinner recently. I brushed off the tux and polished my shoes and called up to make sure that the administration had hired a mashgiach whom I trust. I was assured that the mashigiach would be present and everything would be on the up and up.
When I sat down, and had my first course delivered (a lovely fancy, cooked dish) the mashgiach came over to me and said, "I didn't turn the oven on! This food is bishul akum!"
So I went through the check list of all the exclusions for bishul akum and found none - my meal was completely bishul akum. So sad...it looked nice. [note - for the sake of the hypothetical, please avoid finding reasons that the food is not bishul akum]
Can bishul akum food be taken home and reheated? I don't fully understand if the food is inherently not kosher (the ambiguity over kashering dishes doesn't help and leaves the question of whether one would have to kasher the dishes it was served on, not just cooked in) and whether reheating is part of the cooking "process" at the opposite end from turning on the stove which would turn it acceptable. Would it matter if the food cooled down all the way?
This question looks at the question of the non-Jew "cooking" after the Jew but not the reverse.