The president hopes Thompson can make a difference in a state decided by fewer than 6,000 votes in the last presidential election.
Bush is counting on Thompson's popularity as governor for 14 years.
The state's current governor, Jim Doyle, is chairman of John Kerry's campaign in Wisconsin and is active in campaigning for the Democratic presidential nominee.
The Health and Human Services secretary addressed the Wisconsin delegation at the Republican National Convention in New York Monday.
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