I would definitely keep them in the fridge if you can. I don't know that the ambient will harm them, but if it has any effect, it's not likely to be a good one. I don't have experience with this, but I'd try to keep them under 70 if possible. I'd be pretty sure you won't have a problem up to 65, 65-70 is in a grey area, then I'd start worrying.
Maybe someone who has experience rather than gut feelings will chime in, though.
Actually--would it be an option to cool them slowly in the temp controlled fridge, then move them to an ordinary fridge for lagering? That would be the best, and would free the temp controlled fridge up in a few days' time. Food storage temperatures are ok for lagering.