Aside from widespread panic and confusion, not much. Earth would cool as it does after sunset, and we would be kept warm by the heat retained in the atmosphere, oceans, and land as we are every night.
This is with the assumption that the Sun is simply "frozen" for an hour -- say, a giant bushel is put over it. If you actually turned off all fusion in the Sun, it would collapse and then explode, and then we'd have other fish to fry (although it would take longer than an hour for the explosion to happen). Don't get confused -- the Sun doesn't have enough mass to become a supernova, this would be a different process, which won't happen because you can't turn off all fusion in the Sun. Though there is a small but finite probability that it can stop right now on its own. But it won't. Very probably. Very. But it could.
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