Bigfoot will get knocked out in the first or second.
Let's not forget that bigfoot was soundly beaten and outclassed by Werdum over the course of three rounds.
No mercy summed it up earlier. Bigfoots tactic will be to smother Overeem against the cage, try to wear him out and get the take down. I see him getting shrugged off with relative ease though and just tossed aside in the clinch.
Saying that though, after the Werdum fight, Bigfoot could have it in his head that because it looked like Werdum was having success on the feet (which he really wasn't) he may think that he can actually stand with Reem too. If he does that, he's entering a world of pain.