I'm not an expert on corns, but if the room gets no hotter than 81, it'd probably be ok. I wouldn't offer a hot spot though, at those temps. I wouldn't suggest keeping the corn in the same rack with the balls, especially if you have supplemental heat on all the tubs...that'd be too hot.

Maybe a glass tank in the coolest corner of the room?

If it comes down to the only option being to put the corn in the rack with the balls and nothing else....then I'd turn down the the option to take it.