Bad idea. By mentioning a heat shield, you've implied it's a loud open-frame generator. If I were to run my Honda 2k near something, the only heat I'd be concerned with is the exhaust.
Further, if this is a loud one, it'll be even louder inside if it's that close, up high, and mounted on something that will vibrate. It's best to keep generators out of sight at night rather than any sort of protection devices. But, and I hate to presume, if it's a construction generator you won't have any theft worries.
My apologies if my assumption is wrong.