From Charlie Cook :

So if Thompson does enter the race, who would it hurt? Two recent polls — one by Peter Hart and Neil Newhouse for NBC News and the Wall Street Journal and the other by RT Strategies for the Cook Political Report — indicate that Thompson’s candidacy would draw most from former New York City Mayor Rudolph Giuliani, perhaps about 4 to 6 points. He would draw minimally, if at all, from Sen. John McCain, R-Ariz., and former Massachusetts Gov. Mitt Romney. Thompson would start out behind Giuliani and McCain and about even with Romney.
To be sure, Thompson is hardly a household name. In the NBC/WSJ poll, only 26 percent of Americans knew enough about him to venture an opinion. Of those who knew enough to judge, 22 percent were favorable, 4 percent were unfavorable. Another 19 percent had neutral feelings, which probably means they know little or nothing about him, while 55 percent confessed to not knowing who he was.
The NBC/WSJ poll of 1,004 adults was taken April 20 through April 23. The Cook survey of 1,000 adults was taken between April 27 and April 29.
The NBC/WSJ poll showed Giuliani leading the pack with 32 percent without Thompson and with 28 percent when Thompson was added to the mix. The Cook poll had Giuliani on top with 39 percent without Thompson, and with 33 percent with a Thompson entry.
The impact on McCain, Romney and former House Speaker Newt Gingrich was less noticeable. McCain had 22 percent in the NBC/WSJ poll without Thompson and 21 percent with him as a candidate. In Cook, McCain was at 24 percent without Thompson and 22 percent with him. Romney stayed at 12 percent in both versions of the Cook poll question; in the NBC/WSJ poll, he had 12 percent without Thompson and 11 percent with Thompson.